There are two way in "must".
First,it says:this is your necessity,you have to face it.at this meaning,it has no PAST tense and FUTURE tense itself.
PAST TENSE:I had to do it.
FUTURE TENSE:I will have to do it.
Second,it says:this is your obligation.This is a deduction.at this meaning,it can express a past action: (modal + perfect inifitive) He must have done it.
Another point:
I have to do it.(no contraction)
I've got to do it.(the contraction is always used)