I have a file on the desktop that I want to drag onto a window (my browser). Suppose the browser is fully maximized.
How can I do that in Lion?
Before, in Snow Leopard, I could swipe up (reveal desktop), click + drag the file, then swipe down.
Just ⌘+Tab to Finder, click and hold on an file icon, ⌘+Tab back to Chrome and release the icon. The same technique should work even if Chrome is running in Lion-esque fullscreen mode, and if you are dragging something from the desktop.
If you're having troubles getting to the actual desktop, I do know that the Show Desktop gesture in Lion has changed. You may need to activate/configure it in System Preferences -> Trackpad -> More Gestures, so now "Spread a thumb and three fingers" to view the desktop.