I've only done it from Shenyang. You just go to the main bus station in Shenyang (right next to the North Train Station) and there are busses leaving all the time. It takes a couple hours on mainly expressways to get to Dandong. You could also fly from PEK if you hit the right day, I believe there are 3 or 4 flights a week.

I'm sure the setup in Dalian is the same. Just go to the main bus station in town and they'll get you there.