Minibus/Van - Take a van marshrutni from the Medical University Pjhishkakan Hamalsaran on the corner of Abovyan and Koriun to the upper Avtokayaran. From there you can take a marshrutni headed to Ijevan that will stop in Dilijan on the way.
Taxi - a taxi from Yerevan will cost approximately 10,000 dram $33 one way with a standard meter price. You can probably negotiate a better rate, especially for round trip.
Day tour - many companies offer day tours from Yerevan, which include Dilijan, Haghartsin and Goshavank. They can be cheaper than taking a taxi, and depart in the morning on fixed days of the week.