Okay, so you want to record yourself singing or playing an instrument. Cool! And because you're a very clever pony, you want to get the best deal you can and choose the best mic for what you want to do!
But when you go to your local music store, or browse through microphones online, there are a million and a half specifications you don't know anything about. You don't know what to do!
I plan on changing that.
Instead of forcing you to go through the trouble of Googling definitions and sifting through tons of stuff you don't understand/need to know about, here's a quick guide on recording equipment. As always, if you want to add or change something in this guide, please let me know! I want this to be as informative as possible. ^.^
YOU GET WHAT YOU PAY FOR.
That is the number one rule when it comes to audio equipment. If you shell out $20 for a microphone, you miser you, you'll get a pretty terrible mic that won't get you anywhere near a high-quality recording. Likewise, if you only spend $25 on an USB interface or a mixer, you'll end up with a terrible preamp that introduces all sorts of fuzz into your sound.
Unfortunately, be prepared to spend a lot of money if you want high-quality recordings. You'll need to spend at least $50 on a decent mic -- $100 if you want a professional one. Then, the $25 audio interfaces are absolutely craptastic. The next-least-expensive are $100-$150 and are significantly better.
If you aren't prepared to shell out that kind of cash, I'd highly recommend buying an okay, cheap USB microphone from RadioShack or someplace similar, and saving up for something more expensive. You won't sound as good as if you bought that $40 mic, but in the long run, you'll save yourself a lot of money and frustration. If you don't plan on doing too much recording at all, just get a $50 USB mic and be done with the whole ordeal.
In a similar vein, if you have cash to burn, don't go out and buy expensive stuff immediately. Settle for a good $100 mic (say, a Shure SM57, or an Audio-Technica AT2020 for vocals) and a $100-150 audio interface if you need one, and learn how to set up mics properly before upgrading your gear. While you'll probably ditch the interface later, that mic will probably stay in your arsenal for a long while.
Know your cables.
For the most part, all mics will only use XLR cables. That's simple enough. But when you get into audio interfaces, mixers, and all sorts of other equipment, there will be a ton of different options and limitations as to what sort of cable goes where. So it's a good idea to know something about them.
For starters, the ends of all cables are either male or female. The male jack plugs into the female jack in exactly the way you're thinking about. So when you're looking for conversion cables, cables to convert one kind of cable into another, you'll see things like female-to-male or male-to-male quite often. So that's what that means.

XLR
See the image above. When you're dealing with microphones, this will be the most common one you'll see. There really isn't that much to say about them.
TRS/TS
More commonly referred to by how wide they are (quarter-inch/6.35 mm, eighth-inch/3.5 mm, etc.), these are the cables you know and love. Standard iPod earbuds use eighth-inch/3.5mm jacks, guitars use quarter-inch/6.35 mm jacks, etc.
With these, though, you'll have to be careful whether you're referring to stereo (TRS) or mono (TS). How can you tell? Stereo ones have an extra ring. (All guitar cables are mono, for the record.)
Still yet are cables that have two mono TS connectors to represent a stereo signal. That's something to look out for if you're looking into mixers. (Here's a stereo-to-two-mono TRS conversion cable)
There are also MIDI cables (technically, 5-pin DIN), which look very much like XLR. MIDI instruments require MIDI cables to function (unless they can plug into a USB port), so be careful with that, especially when you're looking at audio interfaces.
As a word of caution, most XLR cables have three pins while MIDI cables have five. However, some XLR cables do have five pins. For the most part, it shouldn't be a problem, but you can never be too cautious.
Lastly, there are USB cables to plug directly into your computer. You should know what they look like.
Know your microphones.
As far as we're concerned, there are two kinds of mics out there: condenser and dynamic. (There are others, but if you ever have to use them, you're probably faaaar too advanced for this silly little guide.) They're different in how they turn sound waves into electric signals; you can look that up on your own if you're interested.
Condenser mics are more sensitive to volume and feature a brighter sound. Because of the way they're made, condenser mics pick up everything. If you can hear it at all, that mic can, too. If things are bad, you might have to look for noise gating software to mute the little stuff in the background, though the absolute best solution is to just find a quieter room.
Unfortunately, that also means that they easily overload, clip, and produce feedback. If you record a sound that's too loud, you get this nasty crackling noise in the recording. It's easier to hit that threshold with condenser mics, so you'll have to make sure the input volume is low enough and physically back away from the mic when you get louder.
Feedback is what happens when a microphone hears itself (microphone-ception!) You know that really loud, piercing screech that sometimes floods the room when someone's onstage with a microphone? That's feedback. The best thing to do is to not use speakers when recording. When you listen to something with speakers, mute your microphone.
Condenser mics are usually also brighter than dynamic mics, and that's entirely due to the fact that condenser mics pick up a larger range of frequencies. They pick up higher sounds pretty well, giving you a more accurate recording than a dynamic mic would. The problem is that they can have some problem recording lower frequencies (especially smaller mics), and if you're too far from the mic, it can give you a tinny, fake sound.
Solution? Don't record far away from the mic, and use some EQ to boost those lower frequencies and lower those higher frequencies later.
Things to watch out for: Condenser mics are fragile, so be careful with them.
If you use one, make sure you can supply phantom power. USB condenser mics get their phantom power through the computer, but if you don't get a USB condenser, you'll have to make sure that your audio interface or mixer can supply phantom power.
Dynamic mics are hardier and feature a darker sound. You can still overload dynamic mics or cause feedback, but it's not nearly as easy to do that as it is with a condenser mic. They're also harder to break; both of those reasons are why they're so frequently used in live performance. They also don't require phantom power, which is nice.
They're also darker than dynamic mics and have a harder time picking up all sorts of unwanted ambient noise. Dynamic mics have trouble picking up higher frequencies, so that gives them a darker, sometimes warmer sound. Unfortunately, that means that with certain instruments, they sound boomy and you'll have to do all sorts of EQing to get it to sound right.
Alright, then, what about pickups? The big thing you should know about pickups are that pickups are not microphones. Pickups don't detect sound -- they detect the movement of the strings above them. Meaning, if you record an acoustic guitar using pickups, it will sound like an electric guitar. Now, there are benefits to doing this. If you have the software to turn that pickup signal into a legitimate-sounding instrument, you can record without the hassle of setting up mics. Not entirely professional, but it works.
But for the most part, unless you are going for an electric sound, record those instruments with microphones, not pickups. Leave pickups for electric instruments.
Directional Microphones
Cardioid? Supercardoid? Omnidirectional? What is this talking about?
A microphone's polar graph refer to where a microphone can pick up sounds from. Most microphones are cardioid, meaning they pick up sounds directly in front of them and can't pick up sounds coming from directly behind them. If you look at a cardioid graph, it makes sense. If you imagine that microphone is in the middle of that picture, pointing up, then where the graph is further from the center is where the mic can pick up sound better. As you can see, the mic can pick up sounds coming from in front of it, but not behind it.
There are two variants on the cardioid pattern: supercardioid and hypercardioid. They're both similar to cardioid, where they'll mostly pick up sounds from in front of the mic, but supercardioid and hypercardoid mics can also pick up sounds directly behind them, hypercardioid moreso than supercardioid.
There are also figure-eight mics, which can pick up sounds directly in front and directly behind them equally well (but not off to the sides), and omnidirectional mics, which can pick up sounds coming from any direction.
For the most part, you'll want to go with a cardoid mic if you're just going to be doing some simple self-recording. Omnidirectional mics are really good for picking up atmospheric noises (like natural reverb).
If you're trying to mic a drum set, good luck. There are guides for that elsewhere online. >.>
Right, so I play the _______. What mic should I get?
Really, there are guides for this online -- I hear Google's a good resource. =P I could tell you stuff, but there would be so many exceptions to said stuff that it's hardly worth it anymore.