We would appreciate it if someone teach/teaches us...

Neither. Use "taught". When discussing a hypothetical situation and its result, useing the conditional "would", the simple past tense is used: we would appreciate it if someone taught us how to solve this mathematics problem; I would be rich if I won the lottery; my father would be angry if I crashed the car; my mother would be sad if the dog died.

Thanks, centrox.

I see I spelt 'using' wrongly. This was a typing error, not ignorance!

It's OK, centrox. I knew it was a typo.