How much does it usually cost to reinforce a necklace or to get a better clasp put on it?

that depends on what type of metal we are talking about (silver, gold, costume jewelry), what the reinforcement includes (soldering etc.) or what type of clasp, what metal is needed. You could take your jewelry to a jeweler, but that will probably be the most expensive solution, you can also contact an artisan jeweler which would probably a lot cheaper.