Pianos can be quite tricky. For a few reasons - first of all they have incredible dynamic range. In fact, the full name of a piano is a 'pianoforte' which literally means a 'quiet loud'.
Secondly, they have a wide range of frequencies compared to most other instruments. For example, there is an alto sax, or a bass sax, etc. There is a violin, a viola, a cello, and a bass. To get the full range most instruments need multiple versions. A full sized piano covers a range from 27Hz to roughly 4200Hz.
The middle C and the octave above it is quite a popular range for people to use a piano in. Unfortunately, these frequencies also happen to be where vocals and other mid-range instruments come in as well. Note that the 200 - 800Hz range is also the source of much muddiness in mixing.
Pianos have a sharp attack and can have a very long decay. Combined with the dynamic range, it can be tricky to get the desired volume in a mix without also getting a load of sharp peaks that cause problems for getting the overall loudness desired out of the track as a whole.
Beyond all of those natural qualities of a piano, there is also the fact that because a piano is such a familiar instrument, it is really easy to hear when the MIDI has not been programmed well. No matter how good the samples used for the instrument are, getting the natural flow of someone playing the piano can be very fiddly.
Having said all of that, here is a piano piece that I did just over a year ago. I think I got as close to realistic as I could given that the piece is entirely generated in Max 6 (it's now up to version 7). It was a generative piece based on probabilities. The patch I wrote fed MIDI pitch and velocity data into the Steinway grand piano in Logic Pro 9. The patch has a small bit of timing 'error' built into it so that everything isn't exactly on the beat.
As for the sound itself, the processing chain goes like this:
Piano Track (EXS24 (Sampler) - Steinway Grand Piano) :
Subtractive EQing: Low cut at ~65Hz (Wasn't using the lowest notes), cut at around 390Hz (may have to move this around a bit) another at around 1000Hz. These cuts are relatively shallow and wide ~-6dB 0.5Q. Subtractive EQ before compression to avoid emphasising unwanted frequencies. No additive EQ before the compressor because I don't want to trigger the Compressor with 'false' peaks.
Compressor: I want to let the peaks through but get the decay up a bit. Att: 6-8ms, rel: ~180-210ms, rat: 2:1, Thres:-12dB (with the original peaks being somewhere ~-6 to -9dB.
Short reverb: This is to emulate the sound of the piano itself. The frame, case, and soundboard of a piano have a bit of reverb to them. This is very short, maybe ~200ms decay and is mixed very low. Let the dry signal through 100% and add the wet until I can hear it, then reduce it until I can't hear it (repeat until I've found the exact point at which it is going from not audible to 'just barely audible') then reduce the wet by a decibel or so. Why make it inaudible at this stage? Because later it will get compressed again and it will be brought up and I want it to be very subtle.
Additive EQ: Small bump (~1.5dB) around 200Hz for more body. I don't always use additive EQ.
Limiter: People say not to put a limiter on every track. I expect this is because people have a tendency to abuse limiters. Used well, they will not be noticed. At this point, I just have the limiter there to knock no more than 1dB off of any rogue peaks. The other benefit of this is that if your two stereo channels are a bit out of whack as far as amplitude, you'll even it up a touch - this is not to make it mono but to prevent a 'lean'. Pianos are tricky and most MIDI versions I've used place the notes in the stereo field to correspond roughly with the way they are laid out on the keyboard which is nice because you get a nice wide piano sound, but if most of your notes are higher or lower tones, it sounds unbalanced.
FX Bus (send, aux, whatever):
Bus 1 is for delay.
EQ: High pass. Lower sounds sound like shit when they are echoing all over the place. High pass to your own preference. Personally, I don't like letting much below 150Hz through here.
Delay: A very short delay. This is for the slap back off the 'walls'. In the example I gave below you can barely hear it throughout but it's obvious at about 17seconds into the track. I don't remember the exact setting I used there but it's probably ~30 to 50ms. Something longer than used for the Haas effect, but short enough not to sound like an echo rather than a reflection if that makes sense.
Bus 2 is for room reverb.
EQ: Similar to the delay bus. Too much low sounds like shit when it gets into the reverb. Just muddy and blurry.
Reverb: I used quite a long reverb. This one is not so subtle as the other. This is the room, so I usually just close my eyes and kind of listen until it sounds vaguely like what I imagine the room in my imagination would sound like. This one sounds to me like an empty jazz club or something. Leftover smoke in the air. Just one guy and a piano playing for the hell of it a little while after the doors have been closed and everyone's gone. Whether anyone else can hear that, I don't know.
And finally the mastering stage (although I did a bad thing and just had this on the master bus) :O :
Saturation: I like waves AX for emulating analog sound. It can be abused like anything, but it can give good results as well. Any saturater can get you close though. These tend to brighten up the higher frequencies and add a small amount of noise to the track. That noise has a kind of dithering effect and 'softens' the edges a bit.
EQ: Subtractive EQ. May not be necessary if everything else was done well. This is mostly down to listening carefully and removing what makes things less clear. A good starting point again is around 390Hz. However, I always have a high pass/low cut here to get rid of any frequencies below the audible range.
Compressor: This is the mastering compressor. I don't like to add any more colour at this point. I already have the saturator above, and the compressor I use on the instrument track is often one which will colour things a bit as well. The starting point for the settings on this compressor is always Att: 3ms, Rel: 200ms, Thresh: -7dB, Ratio: 2:1, Makeup: +1dB. This is meant to be a subtle taming of peaks, not a track crushing loudness-maker. If you want that, this should be separate to the mastering stage. As I mentioned, I didn't quite follow the process on this example.
Limiter: Threshold -0.3db. Brick wall. Just preventing anything from clipping. If your peaks are not hitting -0.3, you can add a gain in between the compressor and the limiter. If you have to use more than ~3dB gain at this point, you should probably go back and get the gain in stages, starting from the instrument itself. (Gain staging).
tl;dr - I spent a lot of time typing this. Don't want to read a wall of text? That's ok. Have a nice day. :)