Most 12 tone pieces use only 1 row. That is, a 12 tone row. These are sometimes chosen at random, and sometime's they are not.
They're called 12 tone rows because they use all 12 pitches. In a certain order.
You must use these notes in that order throughout the entire piece. Sort of.
You can also go backwards, from the end to the beginning, which is called a retrograded row.
And you can transpose.
You can use chords, if the notes in the chords are the next however many pitches that are in your row.
You can also invert the row. Say the first not is C and the 2nd is G. The inverted row would start on C and go to A instead. The same interval, opposite direction. Repeat for 2nd and 3rd, then 3rd and 4th, and so on.
Inverted rows can also be retrograded, making retrograde inversion rows.
So there's 4 kinds of rows that are derived from the original, the original, the reversed (retrograde), the inverted, and the retrograded inverted.
And all 4 of these can be transposed, so that's 4 x 12 = 48 rows you can use, just from the one you chose in the first place.
You can play more than one row at once, obviously, and you can switch hands or instruments, depending on what you're writing for.