I lived there for a few years when I was younger, but went back 2 years ago as I took my GF as a birthday present.
Some of my tips would be just to walk around the old town. Walk Wencelas Square to Old Town square. Walk along the river to the National Opera house.
Go over Charles Bridge and up to the Castle, you get great views of the city from up there, also worth a look around is St Vitus Cathedral.
There is also a tower at the top of Petrin hill that has the best views of the whole city. You can either walk up or get the fenicular train.
Getting around wise the Trams are really good for getting round, good way of seeing the sights and getting around quickly.
Drink plenty of the local beer – I like Krusovice. Sample the local cuisine – The dumplings are actually really good.
Buy a guide book is the best tip though because as you walk round theres so many things youll wonder what they are that the guide is a great idea.