how do i check continuity without having a multimeter to find out which one of my white wires are hot and I need to hook my black and blue wires to ?
Go purchase the correct tools to do the jobs safely, rigging up some makeshift test device won't solve your problems and could end up injuring or killing you so please ignore those types of answers.
Get a basic multimeter from the hardware store please, read the instructions, and only work on confirmed dead wiring. It only takes 0.01A to kill someone and you're working with 15A-20A here.
As noted in another answer, "Checking continuity" and "finding out which wire is hot" are two very different things.. What you really need to do is "find the hot". Which is something you will often need to do for safety's sake - i.e., to make sure a circuit is really "off" before working on it.
Use a non-contact tester like:
There can be False Positives (induced voltage from nearby wires) and possibly False Negatives (though hopefully very rare with a quality tester - and you can double-check the tester every time you use it by holding it next to a known hot). But a non-contact tester is a safe way to check things out - e.g., check a wire to see if appears hot, turn off the breaker that you think controls it, check the wire again to make sure it no longer appears hot.
A good multimeter is very helpful for checking continuity and for a lot of other things. Which is why they are often sold bundled - e.g., a combination pack of tools like this:
You should make sure the tools are properly designed, insulated, etc. The easiest way to do that is to look for a UL listing. For example, personally I would avoid an item such as this one:
So many "red flags" on that item that I'd watch out for a herd of bulls...