Here are some ideas and answers to your questions (some of these answers may be repeats, so sorry for redundancy...)
1) What do we need to start a team
As EricH said, the necessities include students, a workshop, funds, and mentors. Get some students who are interested in this area of work, funds from sponsors, mentors can come from nearby companies or teachers from nearby schools.
As for a workshop, I can't really think of a possible options. We use a workshop in our high-school that is used for engineering classes. I don't want to say to ask the high-school for permission to use the workshop, but if you find a teacher that is equally stimulated to start a team, you could make a team in the high-school, thus giving you students, a workshop, and maybe some mentors too.
2) Where to look for sponsors
Look in the area. Your best bet is to find a company that is pro-engineering, pro-science, pro-technology, etc.
3) How to go about getting sponsorships from companies
That is not an area that I am strong at, so I will be honest in saying that I could not tell you. I'd rather not say anything, if I cant offer anything significant.
4) How to Recruit team members
For your first year, show students at a school some promotional videos about FIRST. Gather some action-packed match footage to get kids excited and interested. From a student perspective and knowing what students think on the outside, I think students will join if they find it interesting. Don't get me wrong, you will/should get students who are interested in robotics, but add a little extra to get some other kids who are sitting on the fence, persay.
*For years onward, bring the robot to the showings and meetings, so they can physically see what you guys do in FIRST. Its something extra to what was previously stated.
5) How to Organize the team
Have a schedule and assert leadership. Have meetings in a standard location (a classroom works well). Contacting everyone is important as well; If students want to sign up for the team, ask them for email addresses, and tell them to check their email often. Facebook is an excellent alternative as well (I do a lot of team-related communication through Facebook).
6) Anything that might help us start the team
As Andrew Schreiber said, take a look at what other teams do to get some other ideas as to "what to do." Go visit a local team during the build season, and see what they do; maybe you will get some ideas from them too.
Have fun with this. If you have fun, people will be more likely to come back the next year.
Hope this information helps! Good luck with the team! If you have any questions still, Ill be happy to answer them.
