I think everybody got everything I was going to say.
GPS is great--I love it, and would never bash it.
That said, learning to navigate without it is essential. And if you learn to navigate by compass and by stars and sky, you'll
blow people's minds when you
do have a GPS unit up and running. GPS is a tool: no more, no less. And when you have the basics and intermediate skills down for navigation, the stuff you can do with GPS is more powerful.
That said, there's no substitute in my experience for getting out a compass and a map and doing it. It will be tedious at first, and even dumb at times, but it all adds up.
As everyone said, practice basic bearings, drawing yourself out some waypoints and following them to a destination. Easy? Sure--but you can teach yourself how accurate you are at counting paces and estimating differences. By getting out there and doing easy orienteering tasks, you build a foundation by which you can do very advanced things. Like dead reckoning, which is the ultimate test I hope you never need!

But if you're in the middle of an open field, dense jungle, empty desert, or on the wide open sea, you'll be glad you learned it.
Then, learn the intermediate techniques, like resection and intersection. These are incredibly useful things.
Finally, look to navigation without a compass. Learn to read shadows, identify key stars, etc., and you'll be adding immense skills to your skillset. You may never need them--but like I said, if you learn them, they make the stuff you already know so much more powerful.