Speed tests abound on the Internet. Some are more complicated than others and their accuracy can be questionable. I like the speed test at dslreports.com. You don't even have to know what kind of service you have. Just pick a city you want to test against.
Picking a nearby city is fair for testing the claims ISPs make. It errs on the side of the fastest conditions under your ISP's control. Picking one far away subjects the speed to more distance and more interference from other carriers, but can really prove the muscle of your ISP.
Before you start the test, shut down every application you have running and close any tabs. That goes for every computer on your home network. If you have anything else using your bandwidth, then the test application will register a lower amount than you actually received.
Once you're ready, click on your chosen city. The app will use dummy data to measure the latency, upload, and download data transfer rates. You'll see a mark on a graph for your results, compared with the results of others who used the test. This can be filtered by ZIP code and ISP. If you filter by ISP, you can see what speeds others have reported, and use that as a check against a company's claimed speeds.
Now remember, you'll never get exactly the rate advertised, because bandwidth is usually shared. In cable systems, it's shared with your neighbors, so the speed may fluctuate wildly depending on how many people are using it when you test. Even with Fios and DSL connections, overall network traffic can impact your speeds.
So, it's best to do a few tests at different times, and even from a few different services. DSL Reports offers a directory to worldwide speed tests, including some offered by CNET.