There are three main forms of public transport in Prague. The Metro (underground/subway), Trams and Buses.
We have pages dedicated to these services:
You must have a valid ticket to travel on these transport systems but considering the quality and regularity of service (including Sundays and in most cases 24 hour operation) it should be your duty to these services to buy your (considerably cheap) ticket! Undercover Public Transport ticket inspectors operate regularly on all services and can demand to see a valid ticket at any time. If you don't have one you will be fined on the spot! If someone stops you and says 'Kontrol' and shows you a red and yellow badge, you'd better show them a ticket or cough up the 700Kc (US$31.01, GBP19.88, 25.34EUR) fine. If you're in Prague for an extended weekend, a five day ticket is 500Kc (US$22.15, GBP14.20, 18.10EUR).
Although single journey tickets are available you can also get passes valid for 1 day, 3, and 5 days which are HIGHLY recommended. Tickets are available from vending machines (take small change with you), selected shops and Public Transport Information Centres.
Single journey tickets cost 18Kc (US$0.80, GBP0.51, 0.65EUR) for a limited-transfer ticket (20 minutes/5 stops on metro, 30 minutes by tram or bus) and 26kc (US$1.15, GBP0.74, 0.94EUR) for a 75 minute transfer ticket.
You must validate a single ticket or a short-time season ticket for 24 hours, a multi-day ticket for 3 or 5 days immediately after boarding the vehicle or entering Metro for the the first time. The ticket is inserted into the ticket stamping machine (the yellow things on posts) in the direction of the arrow with face (arrow) upwards. An improperly validated ticket is not valid. A ticket issued by a driver from his sales machine does not need to be validated. The ticket does not have to be validated again when changing. Allowance for time to transfer is also included within the period of validity. Don't validate the ticket more than once, as overwriting the date/timestamp renders the ticket invalid!
If you're in Prague for more than a short stay it makes sense to get a monthly, quarterly or annual pass - these can be for specific months or quarters (so-called 'classic coupons') or for 30 or 90 day periods starting when you want. 365 day passes can be bought any time in January. One month and longer length season tickets are only available from certain ticket offices. First you need a photocard. To get this you'll need to fill in this form or pick one up at any of the ticket offices listed here with "all kinds" in the "Cards" column. Then you take it, along with your passport or identity card, to any of those ticket offices where they will issue a photocard and sell you your season ticket.
There is much more information available in English on the Prague Public Transport System here.
Ticket validation machine