Though ATP is a district headquarters, the public transport is not well developed, so most of the times you are forced to reach the station in private vehicles or autos.
There are share autostands in the town from where the share autos ply towards different areas. These arranged in the order of closeness to the Railway Station.
1) Tower Clock (600 m): From here you can board share autos towards SKU (via Saptagiri Circle, Old Town, Sangamesh Circle, TV Tower, RDT Stadium) or JNTU (via Saptagiri Circle, Old Town, Sangamesh Circle, Sharada...
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Nagar, JNTU and some go to Old College too, people shout "College, College" for this route don't get confused) or towards the Highway. Most of the times it will be fixed rate no matter where you board and alight (Rs.20 in the JNTU route), sometimes they will drop you at the Railway Station (for some extra money though).
2) Srikantam Circle (800 m): From here you can board share autos towards Gooty Road, Bukkaraya Samudram areas.
3) Saptagiri Circle (you can board share autos towards SKU or JNTU and alight here): From here you can board autos towards Ram Nagar, Bathalapalli.
These are the share auto stands I personally know about, if anybody knows more about them or more stands, please feel free to add them in the comments.