You have 4 party banners. When you select a party, you can modify its members via the unit frame.
Edit: Party membership is exclusive: a hearthling can’t belong to multiple parties, and you can’t select multiple parties at once. However, it’s possible using my [cough, cough, self-promotion] [Mod] UnitFramePlus v1.2 mod to select an enemy and then click a single button to attack with all of your parties at once (or individually click each party color you want to attack with) rather than having to select each party you want to use and direct them to attack the target.