Someone else's boat

There are many charter opportunities, sailing schools and youth training schemes
Probably every sailing club in the world has options to sail without your own boat, whether hire or crewing for others.
Many people, whether or not part of a club welcome volunteer crew ... but there's work to do.
The RYA's "Push The Boat Out" scheme demands special mention.

Charters and schools

Charters and schools cover a great many opportunities from dinghy sailing schools, which is probably the best way to learn how a sailing boat behaves, through skippered or self-skippered charter, on though to tall-ship experiences.

The costs for these can vary quite a bit, but it's important to remember that, for yachts and ships at least,  you're usually paying for full board. Whether that's on the basis of "everyone does a bit" of the cooking and cleaning, or whether there's a paid cook will be reflected in the cost.  "Everyone does a bit" is probably how most yachts are run.

Searching the web for "sailing schools" or "RYA courses" should turn up lots of results, particularly for modern yachts.  I make no secret of being a traditional-boat enthusiast, so my links here are rather biassed.  But at least you'll have an idea for what to search.