Not sure what your electronics expertise is, but if you don't have at least some experience, fixing scopes can be a big hill to climb over.
Firstly, get yourself a copy of the service manual from above and have a read through:
http://www.sphere.bc.ca/test/tek-par...ing-scopes.pdf
If you have one channel working and not the other, it's not likely to be anything high voltage or particularly hazardous. However you still need to be careful around those bits of the scope as it's possible to come into contact with them.
Now here comes the big problem. If you have a broken oscilloscope you need to have another oscilloscope to fix it really.
When I get a scope with a dead channel it's usually one of four things:
1. Dirty switches (alt, chop)
2. Dead chop/alt oscillator.
3. Blown up attenuator or follower.
4. Dying channel switch.
Each of those is easy enough to debug if you follow the schematics and Tek info above.