This is a really broad question, so I'll touch on all the parts only briefly. The assumptions I'm making are:
- by complete beginner, you mean a beginner at recording, not playing piano
- you want to make a high quality recording of an acoustic piano performance
- you want the recording to be digital
The minimum components you need to do this well are:
- a great-sounding, in-tune grand piano
- a room with great acoustics
- at least a couple condenser microphones
- an audio interface (think "professional sound card")
- a computer with a DAW (recording software) installed
- monitoring equipment
What do they do?
A room with great acoustics is, to some extent, subjective. The room needs to be large enough to allow the piano to "breathe". Room height is as important as the other two dimensions. If you have walls or other flat surfaces too close to the piano, sound will reflect too much and smear the recording. They'll also help to build up low frequency resonances, which you won't want on your recording. The room should be reasonably sound proofed so things like trains, birds, garbage trucks, neighborhood children, etc. aren't recorded along with your piano. (Your eyes and ears can focus; microphones, like cameras, get everything.) You'll want good sound diffusion, which is caused by having objects with lots of irregular surfaces. Some sound absorption (the foam wedges or pyramids) to tame higher frequency reflections is usually a good thing, but some natural reverberation is desirable. (Bathroom reverb is way too much; walk-in closet reverb is way too little.)
An audio interface will provide the audio inputs, preamps, and phantom power you need to connect your microphones to your computer and get them working. It will also provide audio outputs so you can connect your monitoring equipment. It also handles the analog-to-digital and digital-to-analog conversion that you will need.
The DAW (digital audio workstation) is a multitrack recorder + mixer in software form. (There is a lot more to it than that. All kinds of editing features, special effects, sequencing, etc. are included in a DAW.) There are many DAWs out there. Some are free. Some are expensive. All will be capable of producing a high-quality piano recording.
The monitoring equipment you'll need includes high-quality studio headphones and, ideally, a set of studio monitors. Essentially, those are loudspeakers which have a flat response. (The "flat response" bit is important because most speakers and stereo systems color the audio on purpose to make it "sound good" to its intended market. You don't want that because you want to hear what's really there. The same thing applies to headphones. You don't want the most fashionable ones, you want the good ones.) Most studio monitors are active nowadays, which means you won't need a separate amplifier. Active monitors and headphones plug directly into your audio interface.
You'll need to experiment with microphone placement to get a good sound and a good stereo image. There are whole books written about that, but you might try to start by putting the microphones in an X-Y pattern above the strings. If you have a third mic, you might want it in the room or under the piano. I've seen both done. Here is a good article about it.
Note that you probably won't get a great sound your first time trying. People who do this for a living have years of experience and training on you. If you're expecting a world-class recording coming from anything but a grand piano recorded in a spacious studio with good diffusion, you're likely going to be disappointed.
A better use of your money (especially if this is a one-off thing) might be:
renting time in a recording studio where they already have the
equipment and expertise to make a great recording
making a MIDI recording on a high-quality MIDI controller or a
digital piano and sending the MIDI to a studio like this,
this, or this, where they'll use a Yamaha Disklavier to render
your performance on a acoustic piano and send you the recording.
If, on the other hand, you're talking about recording a digital piano or a software piano or a sampled/modeled piano patch from a workstation, synthesizer, stage piano, or whatever, you'll do just fine with the budget you have, and you won't need microphones.
