This is how I do it. If it is a negative minus a negative, I combine the two - signs to make it an addition problem. Ex. -3 - -4 makes -3+4. The answer would be one.
If it is a negative plus a negative, keep the sign on the greater number and take away the sign the smaller number. Ex. -7 + (-9). Keep the sign on the 9. -7 - 9. The answer would be -16.