I moved into my current house almost exactly a year ago and have been trying to make it more habitable; it was all lawn grass and liriope and a few trees (three oak, a pecan, a dead maple) when I moved in. You can search ZIP code 75248 for my postings on inaturalist of what I’ve found in my yard (a few things there aren’t from my yard but most of it is).
I’ve also seen a fair number of species I simply haven’t been able to photograph; red tail hawks, mallards, barred owls, screech owl (pretty sure eastern?), hummingbirds (I think it’d be ruby throated in dallas) a wide variety of moths, a ton of caterpillars, skunk…so I feel like I can mention some of what I’ve done.
1st; think what animals need. Food, water, shelter. Figure out ways you can provide that on different scales. Green anoles and house geckos (yah, non-native but I like them) love to hide under the vines I’ve planted for instance. The possums raid my compost heap regularly. I’ve got a wide variety of native plants–including some cultivars–and grasses chosen to provide a wide variety of seeds (the chipping sparrows love big bluestem, so do garden tortrix) and pollen. I’ve got coralbean and turks’ cap that provide fruit . Basically, plant to provide a good variety of food sources if you can.
I keep a brush pile with small clippings; its where I put the bluestem and the turk’s cap cut backs after I cut them back in late winter, and I put dropped branches there. Attracts a variety of insects that my wrens and woodpeckers and cardinals like.
I’ve got a bird bath and a water feature; I keep hoping to attract amphibians with the water feature but no luck yet. The possums and raccoons like it, but so do tons of feral cats.
Then shelter; what can you do to give animals a safe retreat? I enjoy the predators I get–but animals won’t hang out if they can’t feel safe too. That’s part of why I’m so heavy on vines in my garden, and why I’m so big on groundcover (hmm prairie verbena).
Keep in mind though, you have to live there too. Other people have mentioned leaving up dead trees. That wasn’t an open when our oak started dying, because it was blessed huge and dropped some large limbs; it was only a matter of time before one of the ones overhanging the house fell. And, well, I don’t want tens of thousands in repair work or worse, a crushed kid when it crashes through a bedroom roof.