I will indicate the waffling nature of the following answer with the addition of several consonants and an ellipsis.
I waffle for a couple of reasons. The first is that Lion has a built-in method for doing this, but you’re going to have to rethink the way you use your Mac. The other is that full-screen applications can make things more complicated. Let’s take these in order.
The built-in method is Mission Control. If you want to hide one application while working in another, invoke Mission Control, move your cursor to the top-right of the screen, click on the plus (+) button to create a new desktop environment, switch to that environment, and open the application you want to work with. Repeat for other environments and applications. When you’re ready to move to another application, just switch environments.
Another option is to use the Dock and when switching applications, hold down the Option key while clicking on the application you want to launch or switch to. When you do this, the previous application is hidden. However, it doesn’t hide all other applications if some are open. To do this, press Command-Option-H.
Now, about those full-screen applications. When you make an application run in full screen, the Dock is no longer available to you nor do the Hide commands work. Lion demands that the application is everything and it does this by placing that full-screen application in an environment all its own. If you want to switch applications, you must use the Command-Tab shortcut to bring up the application switcher, use Mission Control, or pull the application out of full-screen mode and switch as you normally would. Of course you could simply avoid throwing applications into full-screen mode. Photo Booth launches in that view by default, but other applications launch in the normal view.
I’m quite keen on auto-hiding applications I’m not actively working with, but I find Mission Control cumbersome. You have a few options here. My colleague Dan Frakes recommended Ben Willmore’s ( Macworld rated 4 out of 5 mice ) to me and it’s very slick. With it you can automatically hide inactive applications as well as completely hide the Desktop. Ben requests a donation for his work.
I’m also a fan of James Thomson’s $29 ( Macworld rated 4.5 out of 5 mice )—a palette-based application launcher. Among its many features is the ability to auto-hide all but the active application.