Starting from a new terrain....
Click File-New, select the size and remember the name you saved it under, now close the TE. Open the saved file in the AHTerr folder found in the Editor directory and create a new folder called texsrc.
Now sure your texture is in the correct form, 8 bit .bmp format or 256 color in some paint software.
In the main folder for the editor itself there is a help file, read it at a later date. It will tell you what texture number corresponds to the texture selection in the editor menu. In this case we will name your new texture ntt0001 which should be labeled grass.
After you have relabeled your texture ntt0001 place it in the texsrc folder and your nearly set. Open the TE back up and open the file again, everything with a grass texture should be your custom .bmp. For underwater textures the process is the same with a few exceptions, the name will be wntt0001. Any water with grass texture underneath it will now show this instead of the stock or custom grass .bmp.
Its important to note that when I say grass I mean in the editor, the texture itself could be anything you choose. If your texture shows up as black you have saved the texture in the wrong format, not being in 8 bit .bmp (verses 24-32 bit) is the most common problem
Strip