It's good to want to learn how to work without hand-holding from a third-party library, but that doesn't mean you can't learn from it. jQuery is just a library of straight vanilla Javascript — there is no other language mixed in.
There seems to be this pervasive notion that there is somehow "jQuery Javascript" and "vanilla Javascript," but for the most part, jQuery is just a library of prewritten code that handles a lot of the more annoying parts for you. You can figure out how to do it without depending on jQuery by looking at how jQuery does it and writing equivalent code yourself. The general techniques will mostly be the same.
The biggest differences you'll usually have in your custom code is that you probably won't want to recreate the whole selector engine (which lets you write things like $("div.foo")
to find divs with the class foo). Instead, you should substitute element selection and creation logic more appropriate for your specific case.