The first thing to say is that there are as many different "views" about how to record music as there are sound engineers! This is just mine...
Techniques are usually learned from personal experience and of course gaining the technical knowledge to translate a sound "in your head" into a practical reality. Musical styles, "fashion" (by this i mean the way we look back at a genre, eg "..the 80's sound"), or advancement in technology all have an influence over evolutionary changes in the approach to recording. The great thing is that there is always room for experimentation. With infinite variation of microphone technique, room sound and audio processing, ....there are accepted practices, but no set rules! That being said, for efficient use of time we need to have a structure and planned workflow. You, the client, would not expect me to turn up on the day with no idea about channel layout or microphone choice? Likewise, for you to get the most out of the session, preparation and a clear idea about what you want to do is so important. 
In general I break down the recording process into three distinct phases, namely TRACKING, MIXING and MASTERING.
From a musician's point of view this is the culmination of songwriting and rehearsing your project. As such this is a crucial part of the recording process. Mess this bit up and the rest is wasted! In general the first decision regarding recording is multitrack or stereo pair (maybe with spot mics).
If the recording is orchestral in a "nice" sounding hall then the starting point is always a well placed stereo pair ( maybe also a second stereo pair more widely spaced to cover different client tastes). Microphone positioning is always decided by using the age old technique.... listening! Where does it sound good? More often than not just behind the conductors head. Also for jazz ensemble this technique works well with spot mics for soloists.
For virtually all other musical styles (rock, indie, metal, funk, soul etc etc..) I use multitrack recording? Why...  because it gives us the flexibility to be able to go back and replace one part, or one bar of one part, without the whole band having to play the song again, and the opportunity to adapt the microphone to the instrument to capture an accurate sound. Right mic, right job!.  This normally involves close mic-ing which minimises the effect of the room acoustics.
To achieve separation many studios dictate that each instrument play their part on their own and then gradually build up the tracks whilst listening back to the tracks previously recorded. This is one way to do it and I don't have a problem with it, BUT it takes a long time and often involves playing to a click track  (.. I have yet to find a drummer that can play to a click track and remember where they are in the song). I prefer to separate the instrument amps by space (or even different room ideally) and have the band play as a band, including (cue) vocals. That way every one knows where they are in the song and they "feel" the rhythm naturally. Of course there will be some spill over of sound between mics but this can be minimised by careful amp/mic positioning. If one band member makes an error then we can go back and repair that section, or do the whole part again for just that instrument. As long as everything is still set up in the same acoustic space then it won't be heard in the end product, trust me. In any case I always re-record the vocals "cleanly"(except for live gig of course, although even this could be done at a later date with attention to matching). The clean vocal is really important since the song often hangs on the quality of the vocal and the spill (from the rest of the band) onto the vocal mic will spoil the separation that we have tried so hard to achieve and "muddy" up the overall sound.
So, what to expect on the day? It normally takes me around 1 to 2 hours to set up. I will have a basic plan/track layout as I always talk to the client and ideally survey the recording "space" that we are going to use. Inevitably the drum kit takes some time to get sounding right (I have known engineers take a whole afternoon just to get the snare drum sound right!). Of course the band can help tremendously by changing skins or strings a few days before the session and taking time to tune the drums how they want them to sound. The microphones will "hear" what you hear. Having said that I have "go to" mic/instrument combinations that I know work which speeds things up. If you are not happy with that then we can experiment. I may use "direct inject" boxes for some instruments (eg keyboards) this means there will be no room sound for that instrument. I provide a 6 channel headphone amp which ties everybody together for monitoring. Everybody needs to be comfortable with what they hear, then they can forget that their amp is in the next room! There may be some fine tweaking of mic positions and this is where I need your patience. It is SO important to get this bit right. We can alter the sound a lot during mixdown however, getting the sound as near to what we want to achieve on the initial recording saves time at mixdown and limits the amount of audio processing required, hence ultimate quality. Then, its over to you...!
In essence this is where we pull together the individual tracks back into a cohesive whole. Having taken trouble to separate the individual instrument tracks we have control of each musical part for mixdown to stereo.
After a day or more spent recording we will get to know each other quite well! I try and remain as transparent as possible during the tracking process but of course while we are listening back to parts just recorded I hear your comments and get a feel for "where we are going". Many musicians feel totally drained after 8 hours of concentrated recording work, taking a break before starting the mixdown stage is essential.! I generally do a "rough" mix based on discussions with the client.(this gives me a chance to "tidy" up the raw tracks; part of the process which from experience clients' find tedious at best!!)  It's best to do this a day or two after the recording session. This mix I send out to the "band" by MP3 to listen back to at their leisure. Of course it will raise lots of comments and may not be quite how you want it. No problem! Once you have had time to get your thoughts together then we can arrange a date for a final mixdown session and finish the mix. The useful point of this phase is it sets a "reference mix" to modify, and may speed things up when we get together.
Getting technical for a bit. A good mix can take a while since we are not just thinking about relative loudness of individual tracks. We have to think in terms of frequency spectrum as well as amplitude in the time domain. You sometimes have to "carve" out space in the frequency spectrum to make way for parts to be heard. So, we can solo individual parts and EQ them (equalisation) to make them "sound" right within the mix. We can compress them to limit peaks and bring up the quieter parts to punch through and we can balance the volume of each part to make the song sound whole instead of many individual tracks. BUT each time you make a change to one individual track it affects how the other parts are perceived, so you go back for a second iteration and so on. I like to think of it as a spiral inwards towards the final product. While we are doing this balancing act we also have to think about spatial positioning... left, right, forward, back .. its all possible  eg. do you want an in your face "dry" vocal sound or a "wet"  mix reverb added to push the vocal (or any other part) farther away to get that concert hall sound? At the end of this process the song should sound complete with effects, fades etc.
This is perhaps the least known about part and least understood part of the recording process. I paraphrase a great mastering engineer "Bob Katz" by saying that mastering is where "art meets science". By this stage of the project we have a song, or group of songs, that we have recorded carefully, mixed to your liking and should stand up as a track on an album in its own right. 
In simple terms:- in the digital audio recording and mixdown stages it is generally accepted to use 24bit word length (instead of 16bit) since it gives more accurate analogue to digital (A/D) conversion (ie less distortion) and preserves sufficient dynamic range to cope with the quietest to loudest sounds that a band or orchestra can play! The files can be at any sample rate from 44.1kHz to 192kHz (... don't get me started on sample rate!!). However, the CD format is 44.1kHz, 16bit word length. So, ultimately that is what we have to end up with. Any conversion of sample rate or word length potentially can introduce minute amounts of distortion, this is something we strive to minimise during mastering. (If you are interested from a technical point of view then just Google "dithering" and "sample rate conversion", that will give you some bed time reading!!) This quantisation error/distortion is very low level in the overall scheme of things however, and sample rate conversion software is improving all the time.
Assuming we end up with a group of finished songs for an EP or album then we have the creative decision, generally by the musicians, or in concert with the record company, as to the order of the songs. This can be a very emotional point of the project but needs to be decided at this stage for the finished master.
The real magic of mastering comes in the sparkle added by frequency shaping/harmonic excitation, multiband dynamics, stereo widening and finally limiting that make the final mix come to life. Its the difference between a good recording and a commercial sounding product. Have you noticed how much level they get on commercial CDs? Yea, it's all down to mastering. Quality level maximisers and limiters to control dynamic range and peaks without "clipping". Many mastering houses use external hardware to process the audio, some use software options to do the same job, it all comes down to the "favorite gear" of the engineer. Either way the goal is to finalise the overall sound and dynamics of the music, whilst achieving near to max levels (on the peaks) that a CD will handle and at the same time creating an overall frequency spectrum that translates well from HiFi speakers, to car, to laptop headphones etc. Its not easy and is normally handled by a skilled mastering engineer who will charge for his/her services.
More often than not I am getting asked to finish projects for CD replication so, to this end I have put considerable time into trialling mastering software. I now use a software mastering package, Ozone5 by iZotope. I would not profess to being a mastering "expert". However, many long hours have been spent listening, tweaking, learning software workflow and comparing effect on mixes. Sometimes just burning CDs to listen on many different playback devices to see how the science/art translates! I also use Sony CD Architect, red book format CD burning software. The red book format is a "must have" specific format for audio CD replication. It allows the addition of unique ISRC/UPN subcodes to identify the recording as well as CD text for album/track titles.
What does all this mean to my clients? It means for no extra cost I can finish a project to the tight technical specification required for replication and, ...well just make it sound better.