They have a search bar on the main page now. I searched for 'clothes' and these lessons came up. The three beginner lessons cover all the verbs as far as I can remember. The ones you want to know are きる, はく, かぶる, かける, and つける.
The others aren't too different from English:
to wash your hands
to take out the garbage
to tie your shoelaces
脱ぐ （ぬぐ） means "to take off" or "undress."
Although you use different verbs for "wear" depending on the part of the body (and size of the item), you always use ”ぬぐ” for take off.
If there are exceptions, I can't think of any but would be happy to learn them.
Edit: I remembered an exception. Contact lens. You would use つける when saying you wear contacts, but would use とる to describe taking them out.