select your mesh.
hold down the RMB and go to "materials" then "material attributes"
in the menu that appears on the right go to "colour", there'll be checkered box next to it (or near it)
click the checkered box, and from the menu that opens select "file"
Your attribute menu (right) should now have changed to one from which you can browse for your texture.
Once you have found your texture, open it, and it will be assigned to the model.
If your graphics card supports it, you can now select "smooth shading" and "hardware texturing" from your view menu, this'll let you see what your texture is lookin like.
Now if you open the UV texture editor, the texture should appear as the background to the grid.
