As said, take the 405 or 480 from Tel Aviv (which is better depends on where in Tel Aviv you are staying; the 405 goes from the central bus station and the 480 from the bus terminal next to Tel Aviv Savidor Merkaz railway station). Both buses go every 10-15 minutes. Just turn up and get on the next bus; buy your tickets on the bus, NIS 16 per person one way. Both these buses will take you straight to the central bus station in Jerusalem.
From there you can walk for about half an hour or take the light rail (tram) in the direction of Heyl Haavir and get off at City Hall (the closest station to the Jaffa Gate) or Damascus Gate (self-explanatory). There is only one light rail line, so you can't make a mistake. Buy your tickets in the machine on the platform before you board the tram, and validate your tickets as soon as you enter the tram. Any passenger can show you how to do this.
If you haven't already done so, read this thread about the Rav-Kav smartcard for public transport.
https://www.tripadvisor.com/ShowTopic-g293977-i1733-k10246840-Rav_Kav_smartcard_thread_updated-Israel.html
The same card is valid on all public transport in the country. Load a sum of money on it to use as you like. You can share a card, except on the Jerusalem light rail, where each person needs their own card. If you are sharing a card and using the light rail only twice (once in each direction) or even once because you want to walk one way, just buy a single ticket for one of you in the light rail machine.