Plan a way for your pet to get up and down from the window, both inside and outside the house. Your window probably isn't situated any lower than a few feet from the ground, so for your pet to reach it, you may need to place doggy steps or a small ramp leading up to the window, both inside and outside. If your pet is a cat, it may not require steps or a ramp but just a shelf in front of the windowsill.
Measure the window and cut a piece of plywood so it fits in the window frame. It may need to be 1 or 2 inches narrower than the inside track of the frame so it fits. You can fill in the gap later.
Cut a hole out of the plywood that is large enough for your pet to comfortably fit through and sand all the edges smooth. Attach a pet flap to the top of the hole.
Open your window and slide the plywood into place. If the window doesn't stay up on its own, the plywood will hold it up. If there are any gaps in the frame, fill them with foam insulation padding.