Although many taps are different, the principle to fix them is the same. Most of the time, leaks occur due to faulty washers caused by general wear and tear. You can purchase a pack of new ones at your local hardware store.
As a tenant, you should only undertake this sort of maintenance if you feel comfortable in what you're doing. Further damage could make you liable for the cost of a repair.
Bleeding a radiator is one of those scary sounding chores which is actually very easy and quick to do. Here's a video explaining what to do.