American Regions Mathematics League
The American Regions Math League (ARML) is a mathematical problem solving competition for primarily U.S. high school students.
How to participate in ARML
Find out if your area has a team already. Contact ARML for details. If your area does not already have a team, ask ARML how to start one.
There is a discussion at AoPS on finding and starting ARML teams.
Resources
Books
There are four books of past ARML problems, though some of them are out of print and/or hard to find, but very worth it.