Here you can find some information about the activity itself.
Many places in Oslo offers baby swimming lessons. Most of them allow only one parent at a time in the pool with the child, but some places allow both parents. The water is usually 32 degrees, so it is advisable to bathe your baby in 32 degrees at home so it does not freeze during the baby swimming lessons. You can buy swim nappies at the store, but some places prefer special trunks that they sell.
Most baby swimming courses are in Norwegian, but I´m sure it´s not a problem if you don´t speak Norwegian. Just talk to the instructor beforehand :)
Here you will find information about the places that offer baby swimming lessons:
It´s useful to take lessons as the child learns from an experienced instructor how to behave in the water and not to be afraid to get water in its eyes. However, if you don´t want to take lessons, it is possible to go swimming with your baby on your own. The public pools Tøyenbadet, Frognerbadet and Bøler Bad all have pools for children. The entrance fee per adult is 86 kr (free for children under 3).
Domus Atletica also offers family swimming on Saturdays and Sundays. The entrance fee is 120 kr for non-member adults and 45 kr for children/babies.
In the summer you can buy some water wings and take your little ones "swimming" in the sea or in a lake. See this link for good spots in Oslo.
Here´s an unfinished map of where you can do baby swimming in Oslo. It´s not entirely updated, but it gives you a rough idea :) Click on the bottom to get a bigger map!
View Babysvømming / Baby Swimming Oslo in a larger map