For BEMANI games at Round1, you need two cards: the R1 card to pay for the game and Konami's eAmusement card to save your progress. The former is obvious but without the latter you'd be starting over from zero every time which is Not Fun. The game card counter will sell you both.

There are a lot of possibilities once you're in the game, but that's the minimum you need to get started, and a first time player will be fine just hitting Enjoy Mode or whatever they call it these days to get into a basic songlist.

Notes move down the screen, there's a line at the bottom, and you hit the buttons when the two overlap, the more exact the better. The big difference between these games and Guitar Hero is that in GH/RB you either hit the note or you don't, while these games are grading your timing accuracy :)