Visit CERN (free, advance booking required)
The only free lake experience is walking around it. If you want to sail, things get expensive. One cheap option for just a sample of sailing experience are the public transport boats which connect different parts of Geneva. The ride is short and costs 3 CHF. Most of the captains don’t even check your ticket.
Further lake experience
The Geneva lake is very big so a lot of towns and villages share the views to it. There are plenty of boats and ships (not cheap) and also trains from Geneva which can drop you at some spot and then you can choose to hike/hop on a train towards the mountains or walk along the lake shore until you reach another magical place. We did quite some walking from Montreux to Villeneuve and explored beautiful places along the lakeside promenade for free.
View over Geneva
Fountains with drinking water and free public toilets