Currently every 2 days there is a train leaving at 20:20 at Tbilisi, arriving at 07:00 in Yerevan.
I paid around 51 Lari one way in a four bed but we were only with 2 in it. There were also some kind of dorm-style carriers which will be cheaper.
You can pay in Lari, Euro, Dollar,... at the border. In Lari it will be 15Lari, in Euro it is 6 (they don't accept coins!)