This comes from a guide I posted at Notebook Review:
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So you just got your shiny new RAM, and you can't wait to upgrade your computer. Congratulations! You've been through the decision making process, scraped up the cash, placed the order, eagerly followed the tracking number, and now it's finally in your hands! This is what you've been waiting for!

But before you install those new sticks, close everything up and ride off into the sunset, there's one thing you really, REALLY should do first...

TEST THAT RAM

The sad fact is that RAM can easily get damaged, for a variety of reasons: manufacturing, packing, shipping, or even installing. Most damage comes from static electricity, and the effects of such damage can result in a system that randomly reboots once in a while, or one that won't boot at all. The latter is pretty obvious, but the former is usually blamed on the OS or something else. (Bad RAM is frequently the true cause of problems with Windows)

In any case, you should ALWAYS test your new RAM thoroughly before considering yourself "done" with it. It's also very important to do this as soon as you get it, so you won't miss the return deadline date. A lot of RAM has a good warranty on it, so that's also an option if you missed the window; you'll just have to deal with the manufacturer directly (which isn't really that bad, at least when I dealt with OCZ).

Testing
The best package out there for testing is called memtest86+. The original project, memtest86 (note the missing "+" sign), is still around, but was not updated for a long time. So the memtest86+ guys took over.

Memtest86+ is very easy to use. All you need to do is:

1. Download the file. I'm going to walk through using the "Pre-Compiled Bootable ISO (.zip)" file. You can get that from this page.
2. Unzip the file. There's only 1 file in there, called "memtest86+-X.YY.iso"
3. Burn the ISO file to CD. This is the potentially tricky part. An ISO file is a disc image, and cannot be burned directly to a CD. Your CD recording tool should have an option like "Burn image to CD" or something like that. If you can't find it, you can try the free ISO Recorder powertoy. After you burn the CD, if you put it back in the drive and see the file "memtest86+-X.YY.iso" listed, you've done it wrong
4. Shut down your computer completely, then unplug it. DO NOT DO THIS IN SLEEP OR HIBERNATE MODE!!!
5. I recommend testing the modules one at a time, so if one is bad, it's easy to know which one! Take out all but one of the RAM modules.
6. Plug in the computer, put the CD in the drive and reboot. Make sure it boots off the CD, not the hard drive. You should see a blue screen with a green bar on the top that says: "Memtest86+". There are screen shots on the memtest86+ web site so you can get an idea.
7. Now, you wait for the test! The test will run forever until you stop it. You should run it for at least 1 full pass, more if you have the time.
8. Once the test is done for that RAM module, shut down, unplug, take out the module you just tested, put in the new one, and test again.

Running the test will take some time, and it's directly dependent on how much RAM you have. One full pass of tests took 45 minutes on my system while testing 2GB of RAM. Don't worry about the time -- just start a test before you go eat dinner or something. My experience has been that bad RAM shows up pretty quickly, but it's worth it to run at least one full pass. I often let it run all evening if I'm off watching TV or something.

What am I looking at here?

• In the top-left, you'll see some information about your system, CPU, total RAM, Chipset, etc...
• In the top right, you'll see the overall progress of the tests. Memtest86+ runs many different tests on the RAM, and when it completes the whole battery of tests, that is considered one complete "pass". So the top bar is the progress of the whole "Pass", while the next "Test" bar is the progress of the current test. Underneath that "Test" bar is more information about the current test that's running.
• On the bottom half of the screen is information about the memory that it's testing. The most I really pay attention to here is the "WallTime" column, which shows you how long the tests have been running.

Dealing with Errors
If you get errors, it will be pretty obvious. The part of the screen that's currently blue and empty will fill up with RED error messages, you can't miss them. What the errors are really doesn't matter. All you need to know is that it's bad. A good RAM module should have zero errors.

At this point, all you can do is return the module to where you bought it, or get a replacement under warranty. There's no way to fix it, and there's no reason to live with it either. Do not put up with a bad module, get it replaced. Replacing it is the only way to make sure manufacturers don't get used to the idea that their customers will put up with bad quality.

Typically, all you need to say is "I tested it with memtest86+, and it was bad." Any memory manufacturer will know exactly what you're talking about, and shouldn't give you a hard time. Some places will cross-ship you a new one, while others will wait for you to send back the broken one before they'll replace it. That's just the way it is.

How important is this?
Personally, I've had about a 40% failure rate with the RAM I've purchased. Maybe I'm unlucky, or just have a lot of static electricity around, but I've almost always had to return at least one of the modules I've received.

RAM is one of the really base components in your system, and if it's bad, you will not be able to have a stable system, period.

If you have other questions, you can take a look at the memtest86+ F.A.Q.