I'm no longer a team captain (phew) but was for years with my previous team, & step in sometimes as field captain when needed with the current lot. I've divided the list below into team captain (T) & field captain (F) responsibilities in case you're lucky enough to have both & not be expected to do everything!
Recruit players (T)
Get the squad together for every tournament/diary matching etc (T)
Team finance (T, but can be delegated)
Arranging/Negotiating sponsorship (T)
Arrange team discounts if possible from suppliers (T)
Do tournament entries (T)
General communication between tournaments (T)
Attend captain's meeting at tourneys (F)
Ensure everyone is ready to go on the field in time for each game (F)
Do the coin toss before the start & final decision if choosing ends (F)
Final decision on team selection (if you're lucky enough to have spare players on the day) for each game (F)
Game strategy (F)
Raise any game issues with the field marshall (F)
Agree & sign the score sheet (F)
Discussions with the ultimate marshall if needed (F)
Keep check on everyone's mood during the day, ensure everyone is happy as possible (F, T)
Organise the staging area during the day, e.g. who does what like gassing, potting etc (F)
Collect any trophys, remembering who needs to be thanked if lucky enough to win anything (F)
Scary long list, now you know why many people avoid it once they've had a taste of captaincy, and delegate as much as possible if they are stuck with it.
Qualities required for both types of captain include :
Endless patience (T, F)
The ability NOT to shout at marshalls or argue, even when you disagree with them (F)
Tactical awareness (F)
Mental toughness (T, F)
Able to drop people when necessary, & do it nicely (T, F)
Highly organised (T, F)
Sensitivity to other's feelings (T, F)
You'll have to ask current/past team mates whether I was any good at it, & what I could have done better!
If your question was asked 'cause you are considering doing the job - don't, unless you're a masochist!