Hello, My 2003 Dodge Durango ac condenser is leaking. I purchased a brand new one. My question is how does the old one come off?

 

Disconnect the refrigerant lines. Probably screwed or bolted to either the radiator or the core support. You will need to recover the refrigerant first and then pull a vacuum for a couple hours before refilling. Probably a good idea to replace the dryer since you are opening the system.

 

See page 24-46 in the 2002 Durango FSM. 2002s and 2003s are almost identical so it is good info for you. Don't have the FSM? Many of the Dodge technical manuals are located here (a good link to save):
https://www.mediafire.com/?xu9h0gt9bdcn6#xu9h0gt9bdcn6
If you search down into the Durango folder there is also a smaller copy of the heating & A/C section of the FSM with a title something like 2002heatac.pdf
Enjoy ...