Is this a draw?


Actually, this is a draw with reasonable play.
Care to post the continuation? My guess is you played g2 at some point, allowing your opponent to play hxg2, creating a passed bishop-pawn and winning.
For starters, there are too many movable pieces.
Usually, that would be true. But rook endgames, being so common, are studied more deeply than other endings. Minev, Fine, and Mueller/Lamprecht cover how to evaluate and play positions similar to the one he posted.

A couple guidelines might be:
- Keep your rook active and causing trouble for the attacker.
- Don't let the attacker created a passed bishop- or knight-pawn.
Here's a quick game I played against Fritz:

Here is the solution of the given position. White h3 pawns exchanges for a black pawn (hxg4) and remains with his g2 pawn. The drawing fortress is Pawn on g2 playing Kg1-h1 and the Rook is on the 1st rank. The point of this fortress lay in the fact that doesn't help if black manages to exchange rooks (on 1st rank - check exchange) because the pawn ending wigh Black oawns Pg3 and Ph4 against white Pg2 is a draw. White just plays Kg1-Kh1. Also, even if black exchanges white g2 pawn Rook ending with only black's g pawn remaining (or h pawn the same, of course) is also deaw - postulates of rook endings, but again, this considers white king on g1-h1 and rook defence on 1 rank.