In all versions of Mac OS X prior to Lion, re-sizing a window meant either clicking the green "traffic light" button in the upper left corner or clicking and dragging the bottom right corner. Windows switchers in particular have found this a frustrating departure from the behavior in other operating systems, where you can generally resize a window from any edge.
Switchers (and the rest of us) can rejoice now that OS X Lion is out, because in Lion you can resize a window from anywhere along its edges, not just the bottom right corner. Simply point your mouse pointer along a window's edge, and it should change to two opposing arrows indicating the direction in which the window can be resized. Clicking and dragging a window's horizonal or vertical edge will resize it horizontally or vertically. As in earlier versions of OS X, clicking and dragging along the corners will allow you to resize the window in both dimensions at once.
Also new to OS X Lion are optional modifier keys while resizing a window, as described by developer Daniel Jalkut. Holding down the Option key while resizing will cause the window to expand in equal dimensions on both sides at once; in other words, holding Option and dragging one horizontal edge will cause both horizontal edges of a window to "grow" simultaneously. Holding the Shift key while resizing will cause the window to retain its current proportions while resizing, so if you have a window that's perfectly square or a 4:3 rectangle, it will stay that shape even as you shrink it or make it bigger. That may come in particularly handy if you do a lot of graphics work on your Mac and want to keep your windows' proportions constrained when resizing images.
This is not to be confused with the double arrows you may see in the top right corner of certain apps' windows, like Safari, Mail, or iPhoto. Those arrows activate full-screen mode for the application and cause it to fill your Mac's screen. If you activate this feature accidentally, reverting the window to its original size is easy. Move your mouse pointer toward the upper-right corner of your screen, and the menubar should roll down, revealing a blue icon with white arrows facing each other. Click that icon to exit full-screen mode and restore your window to its original size.