EDIT 1/31/17 - All of the P/T/Z G2 SDI model cameras now shipping will have PoE built in.
No need for any adapters, just power it using a POE switch.
The PTZOptics cameras are a Class 3 "Mid-Power" device using 802.3af.
The average load usually falls between 7 - 9 Watts in testing during actual use.
The information below still applies to all USB model cameras and all P/T/Z G1 models. 

The first generation PTZOptics P/T/Z cameras and all USB cameras do not have PoE built in,

The ZCam models do feature PoE but it is non-isolated PoE.
This can cause issues when the SDI connection is used at the same time as being powered via PoE.

There are solutions able to reliably add full support of using PoE power without any of the limitations noted above.

The GAF-12v12w from PoE Texas using an EIAJ-04 (adapter H) DC barrel connection attached, also available from PoE Texas, has proven to be an affordable and reliable solution.

The specs for the power connector of the PTZOptics cameras is listed below. 

The power adapter for the PTZOptics camera is a EIAJ-04-Philmore255 connector.

Out side Diameter - 5.50mm

Inside Diameter - 3.50mm

Shaft - 9.90mm

Center Pin - 1mm - positive

Outer - negative