There are plenty of sites, such as the one Dan suggests, to find FSBOs. There's also a popular military one: http://www.militarybyowner.com/ Plus Craigslist. Plus just driving around looking for signs. Plus looking on the MLS--some FSBOs will pay a fee (usually a couple hundred dollars) for their property to be listed on the MLS.
On top of that, there are many ways to find owners willing to sell their properties even if it's not listed as a FSBO. Look for some of my past postings on finding lease-options. The same techniques can be used to find people who'd like to sell their homes when their homes aren't listed on the MLS.
As for "not have it financed," I assume you mean not borrow money from a bank. Sure. There's seller financing. That can be straight seller financing, with a note drawn up. Or it can be in the form of a lease-option or lease-purchase. (Be careful: Texas law severely limits the ability to do lease-options.) It can be a land contract or contract for deed. It can be an equity-share arrangement, in which someone else (friend, relative, investor) puts up the down payment and sometimes part of the monthly payment. It can be a wrap mortgage. Or it can be a "subject to" in which case the owner deeds the property to you and you, in turn, promise to make the owner's mortgage payments.
Some of these techniques use Realtors--there are a number of ways to find possibilities on the MLS. Others don't. I'd suggest you find a Realtor who knows and understands creative techniques for finding and financing properties. One place to start are real estate investment clubs in Texas. You'll likely find some Realtors who know and understand creative financing and more. Here's a link: http://www.creonline.com/real-estate-clubs/tx.html
Hope that helps.
While not search friendly, it would be a good place to start.