start with a, i, u, e, o (yes the vowel order is different in JP.
then do ka, ki, ku, ke, ko
then sa, shi, su, se, so
etc. Learn to write them. Use flash cards to help. Also will probably take longer than a day. It is a huge amount of information to absorb through something that may be extremely foreign to how you've been brought up to think.
Also; pronunciation is different as well.
a i u e o
a as in father
i as in eat
u as in the second part of the u sound in cute. not the 'you' sound but the trailing short ooh
e as in feather
o in first faux
I think it's easy to memorize them well within a day, but ofcourse you need to revisit these several times on different days in order to make sure it stays that way.
Btw, it must be extra tough for native english speakers, as everything is pronounced so differently. It's much easier on me, as most of the syllables are pronounced just like I would when I read them "in german".