Just outside Damascus Gate to the Old City you’ll find the bus station. The buses here run to many of the Palestinian cities, including Bethlehem and Ramallah.
The station is just a 3-minute walk down the main street outside the gate, across from the Garden Tomb.
Once at the station, you just grab a bus (typically a sherut/minivan) to your destination. To get to Ramallah, the capital of the Palestinian National Authority take bus #18, just 6.50 NIS. Buses leave frequently (I waited no more than 5 minutes) but usually only when the bus is full.
It takes about 40 minutes to get to Ramallah. You’ll cross through a borderpoint, but from what I understand it will rarely stop your sherut entering the West Bank. There is no passport check to enter. Be sure to check out the graffiti on the separation wall as you enter the West Bank.
Once in Ramallah, you’ll find it’s actually a pleasant place. Talk to some folks, enjoy some delicious coffee. There’s apparently a really cool nightclub but I never got to it.
To get back to Jerusalem, take the same bus from the same station. It'll drop you off outside Damascus Gate again. This time, you will have to go through border control, but as an international tourist, you shouldn't have a problem. Sometimes you can even stay on the bus and they'll just check for your tourist visa.
Written and contributed by travelsofadam