Anshan has an exit on the main Shen-Da Expressway between Shenyang and Dalian. The nearest airport is Shenyang to the north. Train service is frequent on the mainline through Anshan with service to Dalian and Shenyang. Overnight train service is available to Beijing. Long-distance bus service is available at the bus station across from the train station with frequent buses to Shenyang (leave as soon as filled, sometimes as quickly as 15 min after previous bus has left).
If you are in desperate hurry to leave the town, night drivers can be contacted through the taxi drivers located outside the main train station. The main night driver route is from Dalian to Shenyang and in reverse (cost averages Y500-800 depending on distance). Negotiate a rate and then expect to cough up a little additional during your trip since your fare might be sold to another driver along the way (like a relay race and you are the baton).
Buses to just about everty part of town from the area near the train station. Purchase a town map and it should have the bus routes on it. Buses to Qian Shan depart from the street behind the long-distance bus station which is located across from the train station on south side of square (Jian Guo Nan Lu).