For addition:
-Combine all the like terms...
-If the equation is 4xy+17xy-12x, then you add 4xy and 17xy because they are like terms.
-So, you get 21xy-12x. You don't do anything else because there are no more like terms.

For subtraction:
-If the equation is 3xy+6z-(7xy-12x), then you must first change the signs of the numbers within the parenthesis.
-So, the equation becomes 3xy+6z-7xy+12x.
-Combine all the like terms, and you get -4xy+6z-12x.
Hm? That's not what I was taught...
no o.O it's what you were saying... .-.
well actually I'm just talking about the addition...
nvm that lol... I get it now.. but ... you forgot to group them well that made me confused .-.
Hehe, whoops. I don't usually group anymore. ^_^ Sorry.
For example ...
(2xy + 3y - 2) + (5xy - 2y + 3)
                 2xy + 3y - 2
+               5xy - 2y + 3
=              7xy + 1y + 1

1y can be just "y" ...

Add the like terms. Add the integers as usual... 

For example...
(2ab + 3b - 2c) - (5ab - 3b + 2c) Subtract as usual so the signs of the other polynomial will change..
                  2ab + 3b - 2c
-                -5ab + 3b - 2c
=               -3ab + 6b - 4c

Just add and subtract the integers in the polynomials as usual while the variables remains the same.