Towards answering the updated question, its a chicken/egg problem. The best way to justify an expense is to show how it reduces a cost somewhere else, so you may need to spend some extra/personal time to learn something first to build some kind of functional prototype.
Show your boss a demo like "hey, i did this thing, and it saves me this much time [or better yet, this much $$], imagine if everyone could use this how much money we would save"
and then after they agree, explain how it is some other technology and that it is worth the expense to get more training, and training for others on how to do it better.
