Remember that jam sessions are collaborative. The band isn’t there to accompany you. You’re making music as a group!
Don’t take a scat solo unless you’ve studied and practiced scat solos.
Lyrics should NEVER be read, and especially not from a phone.
Know what key you want to sing in. Choose a key that will work for your voice, ideally one that is commonly used for that tune. If you want to sing a song in an unusual key, bring printed chord charts for the rhythm section players with the chords transposed to that key.
Typically, you’ll sing the melody (possibly after a brief introduction). If there is a horn player, they may play fills behind you. After you finish the melody, there will be one or more solos by the instrumentalists. These solos follow the form of the song, so you need to keep track of where in the song during the solos so you can come back with the melody at the right place! Stand off to the side while the solos happen and come back to the mic afterwards. Depending on the tempo and length of the song form, you might come back at the beginning of the song or (in the case of ballads especially), you might come back on the bridge. This could be discussed before you start or communicated via gesture/eye contact on the fly.
Ballads don’t always make the best jam session tunes. Be sure to also learn some medium swing, bossa nova, and up-tempo swing songs.