I need to replace a condenser fan motor for a rudd outdoor unit. The old motor has 3 wires, orange, brown & black. The new motor has 4 wires, brown, brown with white stripe, black & yellow. How should the wires be connected?

First ,you should have bought a new capicitor for the new motor, if you didn`t do it. On the label on side of motor it will tell you which capicitor is needed. Also the same label will tell you how and where to run /which wire
I will tell you the brown and br/white stripe go to the new capicitor you need to purchase
The other 2 wires will go to your contactor,one on each side on opposite end /not the end where your main 2 hot wires are tied to contactor
The salesperson who sold you the motor should have told you about the need of a capicitor

Beware,, be sure on turn off all power going to the condenser unit