Access speeds are typically controlled from their routers or by the circuit, sometimes on both.
In the case of a T1 all 24 channels of the circuit are provisioned for data and the router handles the bandwidth settings. If you decide that you only require half a T1 they modify the circuit to only provision 12 channels and the router is modified accordingly to allow for only a 768K rate.
There are various sites on the web that will allow you to check your upload/download rates and they are free. Keep in mind that if there is a heavy load on the connection the reports will show slower rates. It is always best to test during low usage periods (i.e. evenings/weekends when few people are on the systems).
You can use the DSL Reports site to test your speed. It is free. They also offer 24/7 monitoring for a fee.