I can't always respond to calls on my 510A...how do I listen to the call before calling
back?

From ATT Web site:
While on a call, press the Right Soft Key to enable the speakerphone feature.
Press the Right Soft Key again to disable speakerphone.
Press the Left Soft Key.
Scroll to Mute and press the Center Nav Key to mute the receiver.
Press the Center Nav Key again to unmute.
Scroll to Hold and press the Center Nav Key to hold the call.
Press the Center Nav Key again to take the call off of hold.

how do I turn on speaker phone ?

Hi Bubba. Most of the time the option to turn on the speakerphone during a call could be in the in-call options. I checked the user manual but there was no option for speakerphone.