There are many sites on the Internet that will measure your speed. Most Internet Service Providers (ISPs) have a speed test server right on their own network. Using it is both good and bad. It will tell you what your best possible speed is, but it's not a good indicator of what your "real" speed will be in day-to-day use. There are also a number of speed tests that require Flash. I won't link to those, as Flash is one of the most unsecured - and unsecurable - protocols on the Internet.
I'd suggest that you test your speed using all of these sites, and average them together to find something close to your "real" speed as you use the Internet in your typical way each day. I'd also suggest that you test at different times of the day, since your speed when everyone is on in the evening may be slower than your speed during the day or overnight.
What you see below is by no means a comprehensive list. But it's a good sampling.
There are also speedtest apps that you can download for your phone or tablet.
Please note: Using these will count against any data limit you may have on your phone plan!