Tae Kim puts it succinctly; his grammar guide is a great resource.
By past tense, do you mean plain form or polite form? Or both? Here's some tips for remembering plain form.
With past non-negative plain form, verbs conjugate into past tense very similarly to -te form.
食べる→食べて→食べた (ichidan verb; plain present==>te form==>plain past)
読む→読んで→読んだ (godan verb; same thing)
If you can remember that, you've got past plain form down.
Plain negative past form is super similar to i-type adjective conjugations. for example:
さむい → さむなかった (i-adj; plain present to plain past)
飲む→飲まなかった (godan verb; same thing)
Just change the final u to a and add nakatta.