と does, in fact, mean "and" in most cases (the only exception I can think of offhand would be when placed after verbs, which is loosely similar to 〜ば or 〜たら). Usually it's used when you're defining a group:
[俺]{おれ}は[武]{たけし}と[夏美]{なつみ}と[東京]{とうきょう}へ[行]{い}った。 "I went to Tokyo with Takeshi and Natsumi."
or giving an exhaustive list of something:
[八百屋]{やおや}で[林檎]{りんご}とニンジンとピーマンと[買]{か}うつもり。 "I'm planning to buy apples, carrots, and peppers at the grocery store."
If you're not intending to give an exhaustive list, you can use や instead of と here to imply that there's more you're not including.
し, on the other hand, is for giving reasons. For example, take the following exchange:
A: どうして[学校]{がっこう}に[来]{こ}なかったの? "Why didn't you come to school?"
B: [熱]{ねつ}があったし、[咳]{せき}もあったし、[宿題]{しゅくだい}がまだやってなかったしもうムリだったんだ。 "It wasn't possible, what with having a fever and a cough, and not having done my homework yet, either."
As with when you're listing things with と, even the last reason in the list should have し after it before going into the explanation, if presented. That said, し doesn't have to be for giving a long list of excuses; it's fine to use it to give just a single reason, like in the response below:
B: [行]{い}きたくなかったし・・・ "Because I didn't want to..."