Depends on what type of pool-side access you have but best thing I found was to forget completely about using the lockers and to take everything in a pram. It’s a real pain trying to stuff all your belongings into a locker whilst trying to hold a baby in your arms.
Our swimming pool lets parents put all clothes and changing items into the pram which is then pushed to the pool edge (but not right in!) Makes things a lot easier.
I always make sure that I have a dry towel on top of the pram for a quick wrap up of a very cold baby. Incidently, watch out for your wee one getting cold very quickly. (15 minutes was more than enough the first time for our wee girl.) Now, our little one has a lycra swim suit (a bit like a rash-vest that helps to keep her a bit warmer.)
Be prepared to load your car up, travel to the swimming pool, pay for parking, locate the changing rooms, grab a family changing cubicle, get changed, push pram to poolside, dangle babys feet in water only for the little monster to looked freaked out at all the noisy things going on and to make it very clear that she wants to go home.
Also dont forget “swim nappies.” Pool attendents tend not to like little floating parcels in their nice clean pools.
Its a logistical nightmare but more than worth it when you see them swimming under water for the first time.