First approach the family abd friends of team members. They have the most direct interest in the fortune of the team. Secondly approach businesses adjacent to the venue for the sport as they will likely be interested in incresed attendance having spill-over into their businesses.
Look for local companies that are successful. Before approaching them, figure out what the expected expenses will be, as well as what they will gain out of sponsoring your team. Be prepared to do some legwork and keep expenses reasonable.
Think of restaurants and businesses close to you which cater to families and/or children such as pizza places or auto shops. Go in and ask them about sponsoring a team. Make sure you have all the information you need before you visit.
You should visit local businesses starting with those you visit frequently. When asking make sure you highlight benefits to the store such as advertising on the uniforms as well as getting their name in the paper every time the team competes, etc.