[abecedarius]

The way I learned it was by keeping an actual printed table handy to look at during multiplication problems. For me at least, that didn't take long and never required memorizing "for its own sake" -- I don't know if that'd generalize, since I don't know of anyone else going that way.

Learning by chant or whatever just seemed super boring (and prone to learning sequential access rather than as random access).

The same principle helped for touch typing and dvorak: tape a layout card to your screen at first.

[cyberax]

Back when I was at school, we had the multiplication table printed on the back cover of all students' workbooks. After a while, I just remembered it.

We also had mnemonic chants for some non-trivial entries.