In general, to find pool tournaments, ask the other players. Then go to each tournament you hear about and ask those players what tournaments they know about.
After doing this for awhile, you will learn where all the tournaments are.
Pool tournaments come and go and are not advertised well. Some are listed in local/regional billiards publications. But sometimes there will be a listing and the time of the tournament has changed or they no longer have the tournament. So always call before going.
There are all sorts of tournaments in pool halls and bars. These will vary greatly as to skill level of most of the players, the game played, and the rules. Various tournaments use modified rules, no rules, or strict BCA rules. So ask what the rules are before playing. Some are written, others are not written and will change from time to time.
At every pool tournament I have been to, the players are more than happy to answer questions about the tournament. Who breaks? Rules. How many games you play to determine the winner for each match. Like race to 1, race to 2, race to 3, etc. Or race to 2 on the winners side and race to 1 on the losers side - double elimination. This means you must win two games to win a match, but after you have lost one match, you go to the losers side and then must only win one game to win each match. If you lose two matches, you are out of the tournament. Etc. So ask away!
Some tournaments are on weeknights and will last late into the night. Might want to ask what time the tournament is usually over if you need to get up early the next day. Others are over more early.
Then some tournaments have mostly very very good players. Others will have mostly bar bangers/beginners. Others a mix of players. Once you start winning at an easy tournament, switch to a more difficult tournament. Then you are challenged and will be improving your playing.
BCA rule book...
http://www.poolndarts.com/p-4106--Billiard-Congress-of-America-BCA-Rule-Book-/