In Texas,since about 90% of the land in the state is privately owned,unless you own land or know someone that does,you will need to either lease land for hunting or try the Tx. Parks and Wildlife's lottery to hunt different state owned lands.
Since deer hunting is a big cash cow in this state,you need to find a lease you can afford. You also need to find out if it's a year long lease,or just a season lease. A lot of hunters find out the hard way after paying big bucks for a lease,and it's only for deer season.
I would only lease a year long lease,that way you can hunt/fish/use the property all year long. I pay $2k for a year long lease,and it's split between myself and my cousin.
Check bulletin boards at local feed stores,local papers,small town cafe's for some great hunting leases. If you find a farmer/rancher that has land to lease,offer to help them out doing chores,and it will help you get your foot in the door with them if you are a total stranger.
Most outsiders aren't trusted hunters to these folk's,and if you gain their trust,you can find some great hunting spots.
Texas State Rifle Association
North American Hunting Club