We have tournament announcements on the announcement sheets that are available at each meeting. Also, you can find the most up-to-date announcements and flyers on www.cross-tables.com. If you join the NSA and receive the Scrabble News, there are tournaments announced in it.
Occasionally, players show up for a tournament without ever having attended a club. But usually people go to club before attending a tournament. You will get a lot of support from your club friends when you go to a tournament, and you may attend one whenever you want. Tournaments have divisions, based on ratings from previous tournaments, so you will be in the bottom division to begin with.
After a tournament, players receive a numerical rating based on their performance. The rating is used to give an approximate indication of players' relative skill. The lowest initial rating one can receive is 500 (players can go lower after their first tournament, however). Most tournament divisions are based on rating ranges.