Does anyone know the best way to study for the AMC 10 and the levels beyond that? Stuff like good resources and tutor referrals would be helpful.
Spend time on the artofproblemsolving.com website. They have databases of old contests. The forums are great too.
Sorry for the late reply, but there are LOTS of ways to prepare for this test. I actually posted today about this very subject, I’ll copy and paste what I said right here.
To do better on the AMCs there are many things you can do. For starters, I think you should sign up for the AMC 12 Problem Series offered by AoPS. Since there is a long time till next year’s AMC, I recommend you practice problems from other contests such as Purple Comet, HMMT, PUMaC, MMATHS, etc (as you can see, there are a TON of resources).
By the time September hits, I recommend you start doing all the tests. You should finish all of them comfortably about two weeks before the test so that you can review everything. I can’t stress this enough, but make sure that you COMPLETELY understand every solution offered by AoPS regardless of whether you got the answer right or wrong. This is crucial.
As you start getting better, I recommend you start practicing AIMEs, for they also give tricks and insights into AMC problems (a lot of AMC problems are shortlisted or modified AIME problems).
It’s definitely possible to work hard enough and qualify for USA(J)MO within a year and I know people who have done it (I personally was pretty close to doing this). In any case, good luck with your endeavors in competitive math! Make sure to enjoy it.