As an adverb, "besides" is similar to "in addition." As a preposition, it's similar to "in addition to." Don't confuse this word with the preposition "beside." The meaning for that word is completely different.
1. She doesn't want to move to San Francisco because it's too expensive to live there; besides, she likes living in a cold-weather state.
2. He doesn't mind being unemployed right now; besides, it gives him more time to ride his skateboard.
* When used as a conjunctive adverb "besides" often expresses a benefit in contrast to a negative situation. The first two sentences demonstrate this usage.)
3. Besides windsurfing, he likes swimming and skiing.
(In this sentence "besides" is used as a preposition.)
4. Besides going to the state fair, they've been to the zoo and the beach this summer.
Notice the use of a gerund after "besides." This is very common.
5. Thomas Jefferson was a great philosopher and thinker besides being the third President of the United States.
6. Besides a headache, she also has a cold.
7. He likes to dance but not much else besides that.