Apple added the Activation Lock to iOS 7 to combat the rampant unauthorized reselling of lost/stolen devices. There is no way around this lockout… your only options are to contact the person you bought it from and get (1) the Apple ID login credentials, or (2) your money back. If you bought it from an honest/legitimate seller, they’ll help you out. If you bought a stolen device from a scumbag, you are simply SOL, and you now own a pretty, albeit expensive, paperweight.
If you purchased the device from someone on eBay or CraigsList or a similar site, take whatever recourse you have against the seller to recover your cash.
In the future, Before you buy a used iOS device make sure there is no active Activation Lock enabled that device. Just get either the serial number or IMEI and enter it here. Apple will report the status of the device. https://www.icloud.com/activationlock/