Passenger front turn signal not working. 68 Dart.

Remove bulb, check for power, and check the bulb, for a start

What have you actually done?

If the bulb is good and you don't have power check the correct wire coming out of the TS switch connector

Does the dash indicator lamp function for both left and right?

You can download free shop manuals and wiring diagrams at MyMopar

http://www.mymopar.com/index.php?pid=31