Overview
Your job is to work with the costume designer to repair and/or make the costumes that the designer has chosen. Depending on your time, skills, and interest, as well as the needs of the costume designer, this can look like anything from sewing on a loose button to making whole costumes from scratch. You should know (or be willing to quickly learn) how to use a needle and thread, and it's helpful if you also know how to use a sewing machine.
Timeline
At or around the first prod meeting, you should talk with the costume designer and make sure you're on the same page about 1) your sewing skills and experience 2) how much time you're willing and able to put towards this position and 3) what the costume designer expects from you. It's perfectly fine to tell the designer that you're not comfortable making clothes from scratch. If you do agree to make costume pieces, keep in mind how much time this will take. Depending on the pattern and your experience level, making a dress, for example, will take about 10-20 hours.
If you're going to be making costumes by hand, this should start as soon as possible. You or someone from the costumes team should take measurements of the actors before or after rehearsal. Check Calllboard for rehearsal locations and to see when specific actors will be at rehearsal if you're having trouble catching someone.
As the costume designer finds pieces for the show, they should come to you for repairs. These are typically things like replacing buttons or sewing up a torn seam that can be done by hand. The Ensemble should have the supplies you need (check the sewing supplies box as well as the red Oh Shit box). If not, you or the costume designer can replace these supplies out of the costumes budget.
At some point before Put-In, the costume designer will run a Costumes Parade for the actors to try on their costumes and show them to the director. This is a great time for you to come and see how everyone's costumes are fitting. If there are alterations you can do without an actor around, it's helpful to try to get those done between the parade and Put-In.
During Put-In, in addition to helping move the costumes to the dressing room, you should do final fittings and alterations. This usually involves having each actor come in for a few minutes and try all of their costume pieces on, then making note of what alterations you'll need to do and pinning the clothes to mark where to sew.
During Tech Week, you should be available to do emergency repairs when necessary. It's helpful to bring the Oh Shit box to the dressing room during Put-In, as it has supplies for costume emergencies (it's probably worth checking first though that it actually has things like needles and thread in the important colors).