Just visit the site and click "Begin Test" in the middle of the screen. It will automatically detect test servers near your location.
For the first test, use the server it chooses. Afterward, you can try other servers around the country if you want.
Speedtest.net will measure ping, download speed and upload speed.
Ping measures how fast you get a response back from the test server. The lower the number is the better. If you play online multiplayer games, you'll want less than 100 milliseconds.
As for uploading and downloading, measurements are given in bits per second. Higher numbers are better. Download speeds will typically be much faster than upload speeds
You can compare these numbers against the speeds that your Internet service provider promises you. Be sure to run multiple tests over several days at different times. This will give you on overall picture of your connection speed. You also might find specific periods that it's slow.