What region of the state do you live in? We have a fairly good starting list of
backpacking & hiking clubs in Texas available, including local chapters of the Sierra Club, Nature Conservancy and various birding clubs.
In addition, some parks near you may have their own "friends of the park" clubs that sponsor things like group hikes to do trail maintenance and wildlife census data gathering, and that can be a good way to start hiking with others as well.
Now is a terrific time to get into hiking and backpacking -- weather in Texas doesn't get much better than this and the bluebonnets and other wildflowers are starting to really put on their show!