... I'm making an expense
record chart. I am entering a negative (-) number for
items paid with a credit card and a positve (+) number
for items paid with cash. Hence, I will have both
negative AND positive numbers in the same column ... I
would like to know a formula or use an IF function that
will total up the negative (-) numbers only. ...

One way:
=SUMIF(A1:A9,"0")

(Adjust to your specific range of cells.)