Prague is an amazing city with, I feel anyway, something for everyone. It is fantastically cheap to spend time there, with hostels for about £5 a night and very cheap food and drink. The architecture is amazing, with buildings from just about every style mixed together. The Gothic cathedral that overlooks the city from Prague Castle, the huge number of Baroque and Renaissance buildings, especially in Welceslas Square (Václavské námìstí), the space-age-like pods of the TV mast in Zizkov, and the Frank Ghery "dancing house," to list but a few. (Sorry, but as an architecture student, I may go on about it for a bit!)
The Charles Bridge is the best way to cross into Hradcany from the old town, and is fantastic at night, as it offers wonderful views up and down the river with all the buildings illuminated.
Eating and drinking is a pleasure in Prague. No matter what your budget, you will always find somewhere nice to eat at any time of day. With most places I visited offering a good meal and a couple of beers as well as change for a fiver!
Quick Tips:
Leave yourself several days. I was there for four days and although I saw pretty much all the things I wanted to see, a lot of my time felt a little rushed and I would have liked to have spent at least half a day at the Castle.
Don't overestimate how much money you need. Money goes a long way in Prague, with about 50 crowns to a pound, and there are many cash machines that are usable with most major bank cards. I discovered these were a good way of managing to not arrive back in Germany with unusable currency (as it is hardly worth changing back) as there was only a £1.50 flat charge and I was warned off some of the currency exchange stalls!
Finally, keep your wallet and valuables around your neck or in a bag that you put on your front when boarding trams and trains, NOT in your pocket. Prague has a high petty crime rate, and although the chances of being mugged are very remote, pickpocketing is rife, which I found out personally on the tube, so beware!
Best Way To Get Around:
Internationally speaking, Prague has an international airport accessible from everywhere, and good train and bus services into the surrounding countries. We took the train form Hanover to Berlin, where we caught a train heading through Dresden and Prague that termintated in Vienna. This seven-hour trip ended up costing us only £40, as we are students, and was very comfortable.
Once there, your best bet is a travel pass, costing 250Kc for a week (about a fiver) which gives you unlimited use of trams, buses and the metro that together will get you anywhere you want to go in the city. Passes are checked randomly by plain-clothed transport police, so don't lose your pass!
On the other hand, walking is a good option. I feel the best way to get to know a city is to walk it, and everything in Prague is easily accessible by foot and nothing is a great distance apart.