-Paperwork for robot shipping is very important...if it is a bag-and-tag event, there is a special procedure to be followed but supposedly bag-and-tag is very popular [our team is looking forward to our first b & t this year...heh]. If it is a traditional [ie FedEx] event, paperwork is also really key: if your mentor/coach doesn't have the right papers on hand, your robot may not be delivered to or from the event.
-Make sure consent forms are filled out. We've had unhappy times running around the day of a regional trying to get late consent forms in....your team won't be allowed into the event without them. Have students fill out the online consent forms!! in STIMS.
-Bumpers: our coach says that bumpers are the single most annoying thing about FRC. There are strict regulations as to how big bumpers can be, whether they can be in one piece or articulated, etc. At our regional last year a rookie team showed up and their bumpers weren't right..I think maybe they didn't HAVE bumpers. It was a big delay and nuisance to the team to get the bumpers fixed.
-Don't be afraid to ask for help at your regional. As you'll notice if you attend an event before yours, the pits are always filled with loudspeaker announcements for teams who need tools or parts. Most teams will take a huge amount of pride in helping another team, especially a rookie.
-Like someone above me said, don't neglect the social aspect of competitions. It is always good policy to get familiar with as many teams as you can at an event. Last year we spent an hour in our hotel lobby chatting with a team who was actually from our area, comparing scouting data and such, and we've been so happy to partner with them in several things since.
-Which leads to scouting, a subject near and dear to my heart, as I started out being our team's scout. If you have even one spare person whom you can assign to watch matches and take notes all day, do it. Scouting teams are usually >4 members but I've done it successfully alone for several years.
Even if you don't wind up 'needing' your scouting data [ie you don't get to pick alliance partners] it WILL come in handy. Before every match, I try to brief our drive team on what they can expect from their opponents and alliance partners. When possible, we also try to arrange a strategy beforehand, based on knowing the strongest teams on each alliance.
-Know your own strengths. If your robot is a lot better at scoring than defense, tell your alliance partners! If your autonomous mode does best in a certain starting position, tell them that too. We have usually found that other teams are very willing to work with us to arrange the best strategy for everyone.
Welcome to FRC! Hope you guys have an awesome first season

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Robot is now a verb.
We're back to square one...while we're at it, let's redesign square one!
Team 956: Celebrating ten years of FIRST!
Code:
Team record 2002-2011
2002: Highest Rookie Seed, AOR
2003, 2006, 2012: Xerox Creativity Award, AOR
2006: Semi-finalist, Sacramento Regional
2009: Quarter-finalist, AOR
2010: Quarter-finalist, AOR
2011: Semi-finalist, AOR, and Dean's List finalist, AOR
Personal record:
2008: Lead scout
2009: Lead scout, publicity
2010: Lead scout, publicity, fundraising, Chairman's, videography
2011: Team captain, lead programmer, fundraising, Chairman's, publicity, wrench-turning, Dean's List finalist at Autodesk Oregon Regional