Basic ones - Change the signs of the second integer or the sign of the subtrahend and change the operation, instead of subtraction, the operation will be addition then simply follow the rule in adding integers.
9 - 3 = 9 + (-3) = 6 (Don't mind this, actually, it may only make things more complicated. I'm just showing how 'it' works.)
3 - 8 = 3 + (-8) = -5
9 - (-10) = 9 + 10 = 19
How to add integers (additional info)
For unlike signs, simply subtract their absolute values then follow the sign of the one having the higher or greater absolute value.
8 + (-10) = -2
|-10| - |8| = 2
(It's confusing, isn't it? Don't worry, it's just the same as 10 - 8)
And because the absolute value of negative 10 is greater than the absolute value, the sign of their sum will be negative.