Czech was really fun the first time around that I studied it a decade and a half ago. It has such a great, transparent Latin-alphabet writing system, for one thing. A case system was kind of strange for an English speaker, but it's pretty usual for an Indo-European language. More recently I have advocated for spaced repetition systems (electronic flashcards) like Anki for memorizing vocabulary lists.
First you have to find a good dictionary, like Slovnik (tho I suspect too many people will just rely on Google Translate). I always point to some regular sources, like the Wikipedia entry and Omniglot, although Omniglot has significantly embiggened its catalogue of Czech phrases recordings. BBC Languages QuickFix has a few nice MP3s if you just want some basic essential Czech phrases. The FSI language courses like Czech FAST are often a great free resource, and a country's national broadcaster also often puts out free courses. Radio Praha, the Czech public international radio broadcaster, has the long-running MP3 segment SoundCzech, on Czech phrases through song lyrics. I also love this precious little Web site, the Little Czech Primer.
There are plenty of other Web sites that have spottier information, mostly phrases and commentary: Digital Dialects, czech-language.ca, bohemica.com, Czech-American television lessons (which worked on Internet Explorer on Windows), phrases and idioms. Czech has an interesting system of name days.
And maybe one day I'll get enough Czech to play tarocky. Hodně štěstí!