how to connect hard drive off security system dvr to laptop for data recovery

You can use ESATA or USB(3.0 if you have it) to get access to the drive on your system. You will still need a power supply. Many USB 2.0 and 3.0 to IDE or SATA(make sure your drive is a match) adapters come with a power supply for the hard drive.

Now I do not know what format the system uses, so you computer may not actually be able to see the file system.

Contacting Nightowl may be a better option first to ensure the device uses a file/drive format windows can even recognize. After all you can not pull a drive from a PVR and always have it work in Windows.