The Czech Republic is a friendly country, covered in forested hills, undulating meadows and roads lined with apple trees. Most famous is Bohemia, Sumava for the Czechs, bordering on Germany and Austria. This region of high hills, forests and marshes is the most touristic. But there are other beautiful mountain regions on the border with Poland. Starting from Karlovy Vary in the west there are the Ore Mountains (Krušné hory), followed by the Izera Mountains (Jizerské hory) with their spectacular rock formations north of Liberec. Next are the Giant Mountains (Krkonoše), and the Eagle Mountains (Orlické hory) northeast of Hradec Králové. Further east are the High Ash Mountains (Hrubý Jeseník), and all the way on the border with Slovakia, the Beskids (Beskydy).
KCT publishes excellent 1:50.000 maps carrying descriptions of all hiking trails. These are for sale in regular bookshops. Hiking trails don't normally carry a name or number, just follow your heart. In the landscape the trails are marked using an ingeneous system of stripes. Possibilities for lodging are marked on the maps, there is a campsite in every village, and beer flows more profusely than in Germany.
If you are intent on walking a fully-fledged long distance hiking trail, then follow one of the European long distance trails passing through the Czech Republic. The E3 runs back and forth across the border with Germany and Poland, and includes the aforementioned mountain regions. The E6 passes through the Bohemian forest. The E10 leads straight from north to south right through the capital of Prague. A new project is the Prague-Vienna Greenways, a 400km hiking and biking trail between Prague and Vienna.