1. Familiarize yourself with all tennis and league rules. If you haven't done this already, you will have to do it now. Part of being a captain is making sure the rules are followed and this may mean you have to resolve on-court disputes on behalf of your team. So learn the rules now, before those disputes arise, and then be prepared to back up your team members when necessary.
2. Let everyone know what your “goals” are. If you just want to have fun and the team is laid back and relaxed, let everyone know. If you're hoping to win your division, move up in the rankings, or desperately need to make points just to stay where you are, tell your team members. It not only helps explain what your strategy is, it also lets people know whether or not this is the right team for them.
3. In doubles play, try to pair people up on a regular basis. No matter how compatible two players are, it can take a few games for them to figure each other out. And by that time, they may be down too far to come back. The more players partner up, the better their results should be. While it may not be possible for each member of your team to have a regular partner, try to form groups within the team and partner up within those groups. So you may have 4 players who usually play at Line 1 or 2 and those 4 can pretty much expect to play with each other each week.
4. Keep everyone informed. Let your team members know what's going on so they feel included and can contribute in every way possible. Be sure they have a roster and know everyone's name and phone number, especially cell phone number. Let each member know when and where you are playing. Definitely keep them all updated on how the team is doing each week and where you stand in the rankings.
5. Make it fun. Even when your team is at the bottom of its division, especially when it's at the bottom, make sure everyone is having fun and feeling appreciated. If team members don't enjoy themselves, even when they're losing, they'll find some other team where they do have a good time. So have a team name! Have a uniform! Have lunch together! Have an end-of-season party! Give out your own end-of-season awards! Do whatever you can to develop some camaraderie!
6. Be there for your team. This seems like the easy step but it can often be the most difficult. As team captain, you should really try to be at every match. Of course, you may not be able to be there each and every week. You may actually have to do something NOT pertaining to tennis every once in a while! But, most of the time, you should be there to support and help your team. Your team needs you not just to keep track of the score sheet, team members may also need you to resolve disputes (see No. 1 above) and to “handle” the opposing team's captain and members.