"Felmegyünk" does not mean "we join". What is happening is that both "Felmegyünk az autópályára" and "We join the motorway" mean that we have been driving on a lesser road and are about to drive up onto the motorway.
You could also say "rámegyünk", that is also a common way of saying it.
It is a common way of explaining the action of driving onto the motorway in the UK, I think the best way of explaining it is that you are joining the motorists already driving on the motorway, so you and your car are becoming part of the (usually) bigger flow of traffic on a bigger type of road. Hope this helps? Another comment says that you can join a club/group, but not a motorway, but if you think of it this way, you are joining a group of other motorists who are also driving on the motorway.
I am not sure I am right but I think it should say we MERGE onto the motorway.
I think Felmegyunk means "we go down away" and autopalyara means onto the motorway. So I picture us driving down onto the motorway and in western North American I think we would say "we merge onto to motorway."
To answer peoples questions about the use of the word "highway", this is too general an expression: its any kind of major road open to all traffic. An "autopalya" is quite specific: a limited access high-speed road (gyorsforgalmi ut), with legal restrictions on the kinds of traffic that can use it, like an Interstate (US) or Motorway (UK/Eire). A main road has different terms like fo:ut or orsza'gosu't.