The first method is simple enough -- from the Settings app, go to My device > Lock screen and enable "Shortcuts." From there you can customize which shortcut icons are shown down below on the lock screen, and loading one of these apps up is a simple as dragging it upwards. Naturally, one of the defaults is the camera app.
The second and third ways both involve lock screen widgets, and you'll need to enable them through Settings > My device > Lock screen > Multiple widgets. Once that's done, you can go to Lock screen widgets > Favorite apps or Camera, which controls the widget that appears on the far right. The "camera" option is straightforward enough -- select it, and you get a big blocky camera shortcut, like on the Nexus 4. "Favorite apps" is a bit more versatile, and this allows you to customize a grid of apps -- one of these, of course, can be the camera app.