How do I make random teams fairly?

Paste the names into the Random Team Generator, choose the number of teams, and press Make teams. The list is shuffled fairly and dealt like cards, so team sizes differ by one at most.

14 people into 3 teams gives 5, 5 and 4.

For balanced skill, pick captains with the wheel and let them draft instead.

Shuffle again as many times as you want — each shuffle is a fresh random split.