Measure the width of the window opening, from the furthest outward points on either side. Take the measurement in three different places (top, bottom and middle).
If there's any variation, pick the smallest number. Do the same thing for the height of the opening.
Take your width and height numbers (the smallest of them), and subtract 1/2 inch from each. Use those adjusted width and height numbers to order your order replacement window.
Measure the window when it arrives, to ensure it's the right size.
Remove the thin pieces of trim that border the old window on the edges of the window opening (at the innermost part of the opening, toward the room), using your hammer and prybar. Remove it carefully to avoid breaking it, as you'll have to re-install it later.
Pull the window sashes straight out, toward you into the room. If there's a second strip of trim holding in the upper sash, remove the trim to get the sash out.
Set a strip of insulation on the window sill. Set the bottom of the replacement window unit on the insulation.
Push the top of the window up and into the opening, tucking more insulation in around the sides as you do. Push it until it's up against the border of trim that's around the outside of the opening.
Set a level on the window. Push shims under the bottom of the window and the sides, until it's level and plumb (straight up and down).
Secure the window in place by driving mounting screws through the sides, in the provided screwholes, with your screwgun.
Re-install the border of interior trim so it traps the window in place. Caulk around the perimeter of the replacement window, inside and out, where it meets the trim.