way of swimming; how to swim
Refers to the method, style, or manner of swimming.
He has a unique way of swimming.
The father taught his son how to swim.
Please teach me the correct way to swim.
I learned how to swim at the pool during summer vacation.
I hear he still doesn't know how to swim.
The coach explained the correct way to swim.
泳ぎ means "swimming" itself (the act), whereas 泳ぎ方 specifically means "the way/method of swimming."
Compound of 泳ぎ (oyogi, 'swimming', the continuative form of 泳ぐ oyogu 'to swim') + 方 (kata, 'way, method').