At around 1000 rating it can be good to start studying openings. According to GM Naroditsky, anyway. Many other people say 1800.
About gambits, well:
1. Avoid them with solid opening lines that dont offer much in regards to Gambits. Thats why I answer 1. e4 with 1. ... c6. Safe for a few like the Alien Gambit, there arent too many gambits in the Caro-Kann.
2. Learn them. You can study the gambits known for your favorite openings, and learn how to handle them best. For example I have looked at the Alien Gambit, even if I havent faced it yet.
3. Decline them. This often works if you dont know the gambit. Though some gambits are rather hard to decline. For example Evans Gambit basically has to be accepted.
I a slowly making progress in my rapid games and am starting to see what look like gambits or other what for me are atypical responses in my games. These have tied me up, diminished my ability to develop pieces, make it difficult to make a solid pawn structure, and overall positional weakness. I don't study openings, but try to focus on solid development. Any and all advice on how to handle this is appreciated.