Just assign textures from whichever directory on your computer to the model, export, and zip everything including the textures into your finished add-on .zip file. I'm not sure if it's that simple with the new .zip add-on method but try it out.
If your model appears all silvery it means it's missing some textures. You can double-check in the .zip folder or use the old method:
1- Create a folder with the add-on name. Example, weapon_somegun or item_skihelmet. Make sure this is the correct name you'll want to name your zip folder with.
2- Put all the needed textures in that folder
3- Assign all the textures to your model from that folder.
4- Export and place the result .dts in the folder
5- Select everything inside the folder and compress into a .zip file
6- You're done. You can still edit anything inside the .zip safely if you want, you'll just have to save elsewhere and put it back into the .zip file using "Explore" to open the .zip
This was the old method you had to use before the .zip system was implemented. This is because the modeling program will export the Directory where the texture should be, and not the Texture itself.