That's pretty much it... Remember to observe static electricity safety principles!
1) Read the manual, it'll give you somewhat decent instructions as to how to go about doing this.
2) Make sure your computer is off and unplugged
3) Open your chassis
4) Remove old graphics card (if applicable). There are three common "latches" that are used to secure graphics cards. All are toward the graphics card slot toward the front of the motherboard. One is a sliding latch, one is a bending latch and the other is a "rotating" latch. You should make sure you "undo" this latch. You will likely have to undo a screw or fastener of some kind (depending on your chassis) that secure the graphics card at the back of the chassis. The graphics card should slide out fairly easily.
5) Once the slot is open, if you removed a graphics card, the back of the chassis should have an open slot. This is where your graphics card should fit in. If you didn't ever have a graphics card, there's a good chance the back of the chassis will need to have a cover or such removed. You should consult your chassis manual (or common sense) about how to go about doing this.
6) You should now be able to slot the graphics card in, remembering that the back of the graphics card should line up with the "hole" at the back of the chassis, and the latch on the PCIx / AGP slot toward the front of the motherboard should be such that it is ABLE to allow the graphics card in and latch.
7) Insert the graphics card components / fan DOWNWARDS (this might seem obvious, but I've had people who couldn't figure it out), remembering the notches on the graphics card's electrical contacts should match up with the notches in the PCIx / AGP slot.
8) Fasten all screws / latches / fasteners to make sure the graphics card is secure.
9) Many graphics cards (especially higher end models) require external power. i.e. power not from the PCIx / AGP slot. If this is the case (as stated in your manual, and observed by the physical card), you should use whatever connector is meant to be used. These connectors are usually provided with the card if they're strange proprietary connectors, otherwise the usual molex connector will likely be required.
10) Once everything is in and connected up, you're ready to turn on your PC!
11) The first sign that the card is working is that many cards give a short "splash screen" when you start up. If you don't see this, don't dispair, because there are various reasons you might not see it (it might be a really quick, short duration display, your monitor might take a few seconds to "power up" (in the case of CRT monitors) or the card may not give a splash screen at all).
12) The next sign that the card is working is seen if you were using onboard graphics before. If onboard graphics were using up some of your RAM (as onboard graphics does), then you will now instead see the full amount of RAM during POST.
13) The most obvious sign that the graphics card is being detected (and was actually the REAL first sign) is that you are seeing anything whatsoever. If the monitor cable is plugged into the graphics card, and the monitor is actually showing comprehendable text / pictures, then it's obviously working, somewhat.
14) Boot into windows or whatever operating system you desire and follow the procedures for configuring your graphics card. In windows, this will likely involve popping in the included driver disc (or whatever driver you're going to install), and installing the driver and any utilities you want. If this is Linux, well then it depends what Linux you are using and what graphics card you are using. However, if you're using Linux, I think I can safely assume you know how to physically install a graphics card

15) Once you have configured your graphics card, it's time to test it. The easiest and most fun method (because you're dying to test it out, right?) would be to install a game and play it. You'll be able to tell from the performance whether your card is functioning properly. Likewise, you'll be able to tell from problems that it's not.
16) Enjoy!
A few problems you might encounter:
1) The card does not fit. Many cards are VERY long these days, and if your chassis is quite small, then you're going to struggle to install it. If a hard drive is in the way, try moving the hard drive to another slot. Likewise, whatever is in the way, attempt moving it elsewhere. If this doesn't solve this problem, you're in a spot of trouble! You'll likely need a larger chassis (which is better in the long run anyway, right?

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2) Your power supply might not meet the recommended power requirements for the card. This might not be immediately recognisable, as the card may boot the computer as normal. There are cases, however, where the PC will simply not boot because the power supply doesn't have enough juice. You should check the manual for your card, as well as specifications for your power supply, and compare to ensure that you have enough power for the card.
3) You might receive strange beeps when starting up your PC, or nothing at all. This could be due to a few things, the most common of which are that you haven't inserted the card firmly enough (you should power down and unplug and make sure the card is firmly in place), and that your power supply isn't powerful enough.
4) A host of driver problems that is another thread completely
5) While playing a game or whatever, you are seeing artifacts or strange performance anomalies including random hooking / freezing / BSOD. This can often be attributed to heat and/or insufficient power. You should eliminate these possibilities before declaring the card is DOA.
Unfortunately, there are a lot more variables that can play a part, but these are the most important and I hope they help you to successfully install your card and get gaming!