Crewing on another boat is a great idea to start... perhaps try to line up a relatively short, but several day passage with a suitable candidate..... but that's the big challenge.
These kinds of connections are, esp nowadays, just another 'internet hookup' and what's worse is you may end up isolated at sea with a total whack job and have no escape. So you need to be very careful in that regard.
Buying a ticket to some place like Antigua or some of the other cruiser hangouts and get known locally, try to do some short island hops to get some experience, these are mainly day trips and you can feel your way into the lifestyle. These are generally friendly places, esp amongst the cruising community, and before long you'll have a reputation that will hopefully lead to something more long term.
After a few weeks/months of that you'll have a much better idea of what sort of boat suits you/ that you can afford/ that you actually need etc.
By all means give it a go.. many people 'wait for the right time' and end up losing out.
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)
1984 Fast/Nicholson 345 "FastForward"