By plane: There are domestic flights from Prague to Brno and Ostrava, operated by CSA Czech Airlines.
By bus: A cheap and excellent means of travelling between Prague and other major cities are the buses from Student Agency. These buses are usually a bit faster and cost less than the Czech trains (not considering discounts). On some routes (e.g. Prague to Brno) this is marginal, but on others such as Prague to Karlovy Vary or Liberec, there is no direct train connection so the buses are by far the best option. Usually, you do not have to book a seat but if you travel on Fridays or during holidays from or to Prague, it is recommended. You can reserve seats online at the Student Agency website. Apart from this operator there are many other bus companies that link Prague and other cities and towns, even remote villages, regularly. Most buses leave Prague from the central bus station at Florenc, but other major bus stations can be found at Na Knížecí (metro station Anděl), Černý Most, Zličín and Roztyly, all of which are located next to metro stations.
Local bus travel between small towns and surrounding villages is usually operated by companies named ČSAD (district name), a remnant of the nationwide state-run company Československá Autobusová Doprava from communist times. On local buses you simply tell the driver where you're going and pay him a fare as you get on.
Timetables for both local and long-distance bus travel are available on the IDOS website.
By car: The Czech drivers may seem aggressive sometimes, especially in Prague, but it is far from "madness" as found in some southern Europe countries.
The Czech Republic is a zero tolerance country. It is illegal to drive a motor vehicle under the influence of any amount of alcohol, and violations are heavily punished.
In order to drive on the well-kept motorways, however, you need to purchase a toll sticker. These stickers cost CZK 310 for ten days (for vehicles lighter than 3.5 tonnes, price as of September 2012), but can be purchased for longer periods of time (1 month or a year). If you do not have a toll sticker on your car when you drive on the motorways, the fines can be very steep (CZK 5000 minimum).
Make certain that you purchase the correct toll sticker: there are those for vehicles under 3.5 tonnes in weight and those for vehicles between 3.5 and 12 tonnes. Vehicles larger than 12 tonnes in weight must use an on-board unit ("premid" unit) to pay tolls based on distance.
The condition of many roads is continually improving, but to be economical and fast, drive on the motorways as much as possible, although if you want to get to remote parts of the country you will not avoid side-roads that may be a little bumpy sometimes.
Speed limits in the Czech Republic are usually 130 km/h on motorways, 90 km/h off the motorways, and 50 km/h in towns. Petrol is inexpensive compared to the rest of Europe (CZK 37 / 1,40€), but it is expensive compared to the United States, as it is heavily taxed.
Traffic fines can usually be paid on the spot.
The use of headlights is mandatory at all times. Failure to have your lights on while driving may result in a police fine.
By train: Trains in Czech Republic are operated mostly by state-owned company České Dráhy (Czech Railways, ČD). At Praha–Ostrava line there are two new private operators Regiojet (a subsidiary of Student Agency) and Leo Express  with very comfortable and modern trains comparable to European standards.
The trains go even to the most remote locations of the Czech Republic and unlike buses, they usually operate regularly during off-peak hours and during weekends. However, outside the modernized main corridors, the standard of travelling is often the same as it was in the 1970's, and therefore it is quite time consuming to get to the provincial towns or villages, the trains tending to meander around the countryside.