- Go to the gender relevant changing area.
- Take off shoes where indicated.
- Undress and store clothing. How will depend on actual location but stowing things in a bag and stowing bag in a locker seemed available as a standard option.
- Walk to shower area, either nude or wrapped in a towel or wrap, do not yet put swim gear on!
- Store towel or wrap in pigeon holes provided.
- Take shower and wash with provided shower gel, (according to rules I read also genitals area,) rinse well.
- Put swim gear on.
- Go to pool, where genders are mixed again.
- Swimming is as usual for you, swimwear worn.
- There was a set of signs pointing to sun decks, again gender specific, (likely nude,) but as it was late in the year and cold, nobody used them.
- Other options, like a hot pool or steam room are/might be available, swimwear worn.
- After your swim you return to the same changing area again.
- After swim showers can be taken in swimwear, locals may prefer to undress first.
I used an older pool in Reykjavik and while there were some private change cabins, I never found out how to get the of use them.
Signs what to do came in several languages and/or pictures.
Always check for local exceptions, as mentioned in a comment by kiradotee some pools have mixed showers close to the outside of the area.
The shower area was open, stalls but no doors.
In the Blue Lagoon stalls came with a door and an area to change, also behind the door but the same rules about showering nude and only putting swimwear on later were published on the walls
Most municipal pools ban the use of cameras or other recording equipment in the swimming area, although there are exceptions in areas with many tourists. (From a comment by Jacob Horbulyk.)
I have not been to other pools but found these instructions in several places online as well as in the pool I used.
If in doubt about any of the rules (or where you fit in with the gender separation,) ask. Most people in Iceland seem to speak more than two languages and are willing to help. That included the staff at the desk where you pay.