Catch bus 1 ( or bus 34 if that is more conveniant) from Reykjavik to Hafnarfjörður (280 ISK) which stops for 5 minutes at the main bus station in Hafnarfjörður and then proceeds further into Hafnarfjörður (Bus 1 "Hfj. Vellir"). Get off at the stop Suðurhvammur, from there it looks like a regular highway onramp, but actually it is not a highway, so while you can hitch directly then and there on the onramp it is generlly quicker and easier to just walk onto the main road and walk along that road for a 100 meters or 200 meters until you find a place where cars can pull over.
HItchhiking from the city directly is not the easiet. [[trash: Reykjavík]]