I can't access airplay on my iPad

Swipe up from bottom of screen to activate Control Center; AirPlay should be in there.

If you don't see the AirPlay icon in the Control Center:

1. Turn off router, Apple TV and iPad

2. Turn on router and then wait 30 seconds for it to complete start-up process

3. Turn on Apple TV and then wait 30 seconds for it to complete start-up process

4. Turn on iPad (wait 30 seconds) and test AirPlay

I would have to say that if you do not have Apple TV, then it appears to not be possible.

from apple support site.

Requirements for AirPlay in OS X

An Apple TV;

• Apple TV (2nd or 3rd generation) with software update v5.0 or later. See How to update Apple TV software.
• Airplay turned on in the Settings menu of the Apple TV.