Use modal verbs to make DEDUCTIONS (guesses based on evidence). MUST = very sure (positive), CAN'T = very sure (negative), MIGHT/MAY/COULD = not sure (possibility).
Quick tip: MUST = very sure (positive). CAN'T = very sure (negative). MIGHT/MAY/COULD = not sure (possibility). Base your deduction on EVIDENCE!
MUST = Very sure (positive deduction)
Use MUST when you're almost CERTAIN something is true based on evidence. Very strong positive deduction.
She must be tired. (I see she's yawning - very sure)
He must have a lot of money. (he lives in a large house - very sure)
They must be at home. (lights are on - very sure)
She must have left. (her coat is gone - very sure)
CAN'T = Very sure (negative deduction)
Use CAN'T when you're almost CERTAIN something is NOT true. Very strong negative deduction.
She can't be tired. (she just woke up - very sure she's not tired)
He can't have left. (his car is still here - very sure he didn't leave)
That can't be right. (the math is wrong - very sure it's wrong)
They can't be at home. (lights are off - very sure they're not)
MIGHT/MAY/COULD = Not sure (possibility)
Use MIGHT, MAY, or COULD when you're NOT SURE. It's possible, but you don't know for certain.
She might be at home. (maybe, not sure)
He may have forgotten. (possibly, not certain)
They could be sleeping. (it's possible, but I don't know)
It might rain. (possible, but uncertain)
Common mistakes
Not "She mustn't be tired." — say "She can't be tired.". Use CAN'T (not mustn't) for negative deduction. Mustn't = prohibition, not deduction..
Not "He must has left." — say "He must have left.". After MUST for deduction, use HAVE + past participle (not has). Must have = past deduction..
Practise it
Look at the EVIDENCE! Very sure (positive) = MUST. Very sure (negative) = CAN'T. Not sure = MIGHT/MAY/COULD.