The te-form by itself is just "and" or "by". Xを挟む basically means "to put X between two things" or "to sandwich X", and here "two things" refers to the two teams of a volleyball game. The 5th definition of 挟む in jisho is specifically about this usage:
- to be on either side of (a road, table, etc.); to have between each other; to be across (a street, river, etc.)
彼らはテーブルをはさんで向かい合った。They confronted each other across the table.
(facing each other) across the net in the center of a court (and) ...
This 2チームで is an adverbial expression meaning something like "on a two-team basis". See this, too. English has a word that corresponds to 1人で ("alone"), but somehow lacks expressions that correspond to 2人で, 5人で, 2チームで and so on. So a very literal translation would be "(People) sandwich the net in the center of a court, and (then) mutually hit a ball on a two-team basis".