Software that operates in this fashion usually has a license key. When the software is installed the key comes along with it. A trial version will have a trial license. When the software starts up it checks if the key is valid. Usually, this is done via a connection to the internet where a service will check to see the license.
No date checking is done on the client, it's all through done through the key on a server that no one is adjusting the time on. Change the key, invalid, software expired, invalid, etc.
You can explicitly state that software requires a connection to the internet to work properly over this trial period. Or you can be less rigid and let the user use the software without a network connection and perform checks every so often. That depends on how leeway you want to be with your license during this time period.
Additionally this information that is stored locally (the license) can be encrypted for further protection to prevent tampering.