What is the cheapest and most convienient way to get to beijing from shanghai?

The most convenient way should be the bullet trains between, but most of them are a little costly. Anyway, among them, I know trains no. D312, D314 and D322 is a little cheaper and the fare is CNY309 for a second class seat. For more info on trains, you can saerch at the train page of this website.

It really depends where you are going in BJ. If you plan to stay up north then you are probably better flying.

If you can book in advance then buy an airplane ticket. It's a 1.5 hour flight as opposed to a 5 hour train ride. Plane tickets purchased in advance cost about the same as the train.