This literally takes only a second. Your connection will get a message notifying them you endorsed them, too.
Notice how I suggested you endorse them for only one thing. That leaves room to endorse them for a couple more skills later on. So if you’re going to ask them for a favor—an introduction, perhaps—endorse them for a skill a few days before you make the ask.
Liking and sharing people’s posts and commenting on their LinkedIn Pulse posts can help, too. Also, try to do this even if you don’t need a favor. If you’re connected to someone, hopefully it’s because there’s at least some genuine interest in them or their work.