My bike brakes are lethal, help!
There are a lot of things that could be wrong and a picture of the bike might help confirm this, so I'll just make a list of some things to check and what they need (this is by no means comprehensive):

1) Brake pads -- if they're old, they've likely dried out. Replace them. Needs a hex key. Make sure they're also hitting the rim and not rubbing anywhere. Also, clean the rims with rubbing alcohol (or if you're a student, vodka). 

2) Brake cables -- these can rust or the lining of the cables can be worn out making them not work properly. You need a housing cutter/dremel + awl + file to do this. 

3) Adjust the brakes. They look like single pivot sidepull brakes from google images, and you can find directions to adjust them here. You need probably a hex key and maybe a screwdriver. Also, make sure the caliper is secured to the frame. 

4) The judder could be lots of things -- theres a certain amount of judder on all bikes. Could be a loose headset (is the fork moving when you hold the front brake and try to move the bike?). Or it might go away if you fix 1-3. 

My suggestion is that if you don't know much about bikes or don't have someone to help you is to take the bike to a bike shop to get it checked out and see what needs repair, since you may not have all the tools you need to fix it or the expertise. You need both brakes in case one fails.