The formation of the correlatives is based on a logical table of combinations of two pieces, so in a sense if you can learn all of the pieces you can effectively learn all of the words without having to memorise them. When I was learning them the course book I was using had them represented as a table in the appendix at the back which really helped me to make sense of it. Here is what the table looks like:

However of course you can't really spend the time to think of how the word combines in the middle of a conversation so eventually you will have to remember them instinctively, but it is at least a helpful tool to start with.

Once during an Esperanto event I saw someone teaching the correlatives using a system of pairs of gestures. So there would be a gesture for ki, i, ti etc and that would be paired with another gesture for u, o, e etc. That way you can make a sort of dance to remember them. I think for some people this can help make the formation seem more visual and concrete. There is an old YouTube video explaining the concept here.