In summer, Bern's residents swim in the Aare. The city has several riverbank facilities, but the most popular entry point is the Marzili open-air baths beneath the Bundeshaus. The current here is fast and the river is cold year-round, but from June to September the conditions are manageable and the swimming is one of the most pleasurable things you can do in the city.
The procedure is to enter at the Marzili, swim or float with the current, and exit using the metal ladders along the bank further downstream. The whole river loop from Marzili back towards the Old Town is a common route. The Marzili complex has changing facilities, grass terraces, and a café. Entry is free. If you are uncertain about the current, watch what the locals do and do not swim alone.