I've been to the wall twice, both times to the section near Badaling. There is a public bus -- part of the Beijing transit system -- that you can take to Badaling for not much money. Badaling is nearly always crowded, because it's the closest to Beijing and most developed for tourists. Don't even think about visiting during the May 1 and October 1 holidays, or any other public holiday in China. All you will see are people.

A little further away is the Mutianyu section, about 65 km from Beijing. It's usually less crowded, or so I hear.

There are of course many sections of the wall to visit, but some are in poor repair and might even be dangerous to climb or walk on.

And, while the Great Wall was built supposedly to keep out the Mongols and other invaders, it didn't work.