How to get to shirdi via hyderabad?

There are two daily trains from Secundrabad / Hyderabad to Manmad:

7058>DEVAGIRI EXP from SECUNDERABAD JN 13:30 to MANMAD JN 01:50

And

7064>MANMAD EXPRESS from SECUNDERABAD JN 17:45
to MANMAD JN 08:10

Devagiri Express also goes vis Nashik Road Station.

So, you may either get down at Nashik Road or at Manmad and by travelling another 30-40 minutes by road, can reach Shirdi without much hassle.

Many tour operators apart from APSRTC run many luxury and Volvo buses too.
-------------------------------------Another Way---------------------------------------------
1. By Road (Public Transport): If neither state (AP / Maharashtra) has direct bus-route, you will need to resort to break journey. There is a bus till Aurangabad from Hyderabad. From Aurangabad, you will have quite a few buses running till Shirdi.

2. By Road: (Private Transport) From Hyderabad, proceed along NH9 till Daund. From Daund, proceed on MH SH 10 till Shirdi. Approximate 600km.

3. By Train: Easiest Option is to proceed till Pune by train from Hyderabad and then take the State Transport run buses from Shivaji Nagar till Shirdi. There are a lot of them.