"How do we select students from our team?" There's no right or wrong answer to this. Some teachers nominate or choose students based on class performance. Some schools use a sort of "tryout." Some schools have a sort of "club" with many students, then use performance in that club to choose the team. The main thing to emphasize is that there are two part of the contest that require communication and cooperation, so it's a good idea to consider that when choosing a team (or at least emphasize to the students how important that is).
"How should coaches/teachers run practices?" The first place to start is the "Practice Materials" link. There is a wealthy of information there. Many coaches choose to spend most of their practice time on the Team Round and Relay Round (consult the packet and links above for more info). The students can do the previous year's Individual Rounds on their own, but they can't practice Team or Relay Rounds alone. The important thing is to get the students used to the kinds of tricky problems they'll encounter on the test. Again, the best materials are the big packet, and previous years' contests.
"What awards are given out?" There are 1st, 2nd and 3rd place awards for the Individual Round, and 1st, 2nd and 3rd place awards for the Team Round, and then one "Top School" award for each division. Then each school gets a "Top Individual Award" as well (students who won a higher-level individual award are not eligible for this).
"How are divisions decided?" We mostly use previous years' scores to put each school into one of three divisions. Each school just competes against other schools in its division. If a school is new to the Math Challenge, CMAS and PARCC scores are often used. If you're concerned about your school's division, please feel free to contact us.
"What is the date/time of the contest?" The contest is always the first Saturday in December. We start at 9am (though most coaches meet the students around 8:30 or 8:45), and the Awards Ceremony usually ends around 2:30 (give or take).
"How can I get better at these tricky problems?" There are many, many contests to use for practice and studying. First, do the previous Rich Morrow Math Challenge contests (see link above). Then the Math League has great sample contests. The website "The Art of Problem Solving" has a wealth of information, like classes you can take, and videos to watch, and a fun, free online learning program called "MathCounts Trainer." The important thing to know is that (like anything worthwhile) it just takes time. Be patient and have fun with the math, and you'll learn a ton!