They (typically. Some people tried some crazy things) just went through known passes, which is why mountains are such great natural defenses. If there are only a small number of passes the defending army knows exactly where their enemy is coming through and can wait for them. Many mountain passes (esp. high mountain passes) are not very wide, either, meaning that armies could only pass through slowly and with great care. It is a pretty dangerous business.

I've been talking about the Mongols too much in this sub recently, but they were going on a raid against Russia and decided to cross the Caucasus Mountains in the middle of the winter. Unfortunately there was only one real passable spot, at Derbent. So they had to "hire" (bribe/threaten) guides, but the guides were able to run up ahead and warn everyone on the other side of the mountain that the mongols were coming for an invasion. (Genghis Khan and the Mongol War Machine By Chris Peers). Don't worry, the Mongols win and then kill everyone and terrify all of the Russian Princes for years, but the Mongols also REALLY want to find a better way to get through (they eventually just take over the city of Derbent, which makes it easier).