(The following is assuming you want to do them using Photoshop tools, not Camera Raw where they already exist for you as Rick pointed out)
The Texture slider is sort of a third variation on the Sharpening and Clarity sliders. All three are (generally) about enhancing local contrast, the difference being the frequency of detail they handle. Sharpening enhances very fine detail, Clarity enhances rather coarse details. Texture addresses a range between those two, which has been missing in Adobe software up to now, but was a feature in other software. There are some other subtle things Adobe programs into in each slider, but it's mostly that.
Because those three sliders are about enhancing different frequencies of detail, if you want to reproduce them in Photoshop, you should search for tutorials about Frequency Separation. There are a lot of those. Two older techniques that are sometimes used as part of Frequency Separation are High Pass sharpening (where you can change the frequency by changing the Radius value in High Pass) and the HIRALOAM (High Radius Low Amount) technique with Unsharp Mask.
Dehaze can't be reproduced exactly in Photoshop, because Adobe says it's based on a physical model of light transmission, absorption, and scattering. You can fake it using the techniques people used before Dehaze existed, such as increasing contrast with Curves, and increasing local/edge contrast with techniques such as High Pass sharpening or HIRALOAM.
So try searching for Photoshop tutorials about:
- Frequency Separation
- High Pass sharpening
- HIRALOAM
