Something that I learned when I was 6 and has stayed with me ever since:
0 - 1 - 2 - 3

worst hand is 0 pairs
next is 1 pair
then 2 pairs
then 3 of-a-kind.

The next 2, in this order are:
straight
flush

Which is easy to remember 'cause the best hand in poker is a straight-flush.

The rest are:
full house
quads
straight-flush

(A Royal Flush is just another name for the highest straight flush, and 5 of-a-kind is only in games with a joker.)
For the last 3, I remember that quads is 4 of-a-kind, and that's more then either the 3 or the 2 in the full house.


Hope this helps.