Slide a sharp utility knife in the gap between the window's frame and lower sash. Move the knife around the seam. If the window was painted shut, this breaks through the paint that dried in the seam, allowing the window to open. If this doesn't work on the inside part of the window, repeat the process outside.
Stick a flexible putty knife blade between the window's frame and lower sash from inside the building. Tap the knife handle with a hammer as you move the knife around the sash. This loosens most stubborn windows.
Go outside. Stick a pry bar under a corner of the windowsill. Place a small wooden block under the pry bar. Push down on the pry bar to lift the window up. Move the pry bar across the bottom of the windowsill to loosen it fully.