The whole thing with LinkedIn is for the most part you're supposed to only link with people you know already. That said, there are ways to locate people on the network and to get acquainted.
For instance, you can use the People Search (click the "People" tab) to see if specific people you know are already on there.
On the People Search, you can also search by keywords, company, location, industry, etc. so you can search (for instance) on your town.
You can also look to see if any of your existing links have already linked to somebody you'd like to link with. Browse your links' networks and see if there's anybody else you know who you didn't know was already on Linkedin. That's how I located several of the people I'm linked to now.
If you see somebody in your friends' networks who you don't actually know but you want to request a link anyway, you can use the Invitation feature to see if your common connection will forward your request through to the person you'd like to link with. With a free account, you're limited to five pending invitations outstanding at any one time; you can get more by signing up for a paid membership.
If you pay for one of the premium membership levels, you can also take advantage of the "OpenLink Network." Those who are "OpenLink Network" members may be willing to link up with people they don't know directly.
If you have a paid membership, you can use InMail to contact people directly through LinkedIn, too. That could be a way to get acquainted with people you don't already know, and mutually agree to link.