Accessing Liftmaster controlled garage door from afar
Newer Liftmaster has "MyQ" technology built in.  MyQ is the technology that allows internet control. Chamberlain is a related brand and also uses MyQ technology. 

If your liftmaster has a MyQ logo on the housing (myQ is made to be obvious and easy to spot), then buy Liftmasters internet gateway (Amazon has it) and download the app from your app store.  (iOS or Google-Play)

Most older Liftmasters can be upgraded to MyQ by replacing the wired in-garage wall controller (and purchasing the internet gateway), however I'd call Liftwaster customer service/support and give them your door operators model number and ask which in-garage MyQ controller works with your door operator. (This one works with most models since 1998, and there are options for older door operators too, even a generic interface that works with any brand can be added.)  

(Liftmaster Support is amazing... I wish every company supported product the way they do. They will walk you through any code changes or limit programming over the phone for Any liftmaster opener no matter how old.)

By the way, "HomeLink" car support is something different and has nothing to do with MyQ and internet control. As such, I edited that word out of your questions title.

Screenshot from my phone: