With close to one-and-a-half billion people currently on Facebook, keeping a low profile can be tricky. It's in the site's best interest to make it easy for you to make connections with family, friends, and acquaintances. However, if you want to make it more difficult for people to track you down, there are ways to do it.
From the desktop website, dive into the Settings entry from the toolbar menu, then click through on the Privacy heading on the left. Under the Who can look me up? section you'll find three options that are of use to us here. By clicking on the Edit links to the right, it's possible to stop people who aren't already your friends looking you up via your email or phone number.
There's also the option to hide yourself from public search engines. Turn this off, and your Facebook profile won't appear the next time someone Googles or Bings your name on the open web — unfortunately you can't hide yourself from the search tools inside Facebook, unless you use an alternative or abbreviated name or something like that.
What you can do is limit the information Facebook has on you. Click the Update Info button on your profile, and remove references to workplaces, educational establishments, and places you've lived. This will make it harder for someone to locate you on Facebook, particularly if you've got a common name and are likely to get lost in a long list of search results.
Finally you can go back to the Privacy page and turn off the option that allows anyone with a Facebook account to contact you. Limit this to Friends of friends, and you won't have to pretend to ignore that old classmate of yours who's bombarding you with messages. He or she won't be able to reach you in the first place.