There is an upload function on a website and I want to measure the upload and download speeds from my PC to the website.
Then just time the upload/download to the website in question.
Say you use the 10MB and it takes 70 seconds to upload. Then the speed is 10/70 = 0.142857 MB/s = 146.2857 KB/s
If you just need anecdotal numbers, not exact rates, you can use the built-into Windows 7 "Resource Monitor" (5 Ways to Monitor and Improve Windows 7 Performance). Linux has the rrdtool (Network Traffic Monitoring with RRDTool).
You can always use a bandwidth monitor (e.g.: DU Meter, for Windows).