I use goggles, because if I don't, my eyes will be too sore to see well after an hour's swim, and I drive to the pool.
Whether you have lane markers will depend in the pool, but more have them than not these days, I think. Follow the markers, particularly for direction. If there are no markers, follow the same direction as everyone else in the lane.
If someone behind you is faster, stop at the lane end to let them past. This can happen more in busier sessions, when changing lanes might not work.
I swam at the public pool in Melbourne, and it told you how fast you should be able to swim a lane for each speed. I've never seen this in British pools, and it can vary through the day. Pre-and post-work and lunchtime sessions, fast can be quite fast, with triathletes and madters swimmers. At other times, it's calmer, and I can keep up. If not, I go for medium. I quite often start and finish in the slow lane to warm-up/down. On really good days, I can have a lane to myself. (This tends not to happen in January, but New Year Resolution types will start dropping off now.)
I echo the thought of booking one or two lessons to help your technique and confidence. (When I was a teacher, I much preferred teaching adults to children, as they were usually more motivated and paid attention.)