Decide on your window style. Casement windows are usually easier to open and close (with a crank handle at the bottom), while slider and tilt windows are usually easier to clean (because the glass usually can be popped out and in).
Determine the size of your replacement window by removing the interior trim of your existing window and revealing the rough opening. Measure the height and width of the rough opening and order a replacement window that will fit inside the opening.
Remove the trim (interior and exterior) and cut through any nails holding the window in place (a reciprocating saw works best). If there is a nailing flange on the window, use a claw hammer to pull out the nails.
Cut through any caulking around the edges with a utility knife and remove the window.
Check that the wooden frame is in good shape. If moisture has gotten in and rotted the wood, it will need to be repaired before installing the new window.
Clean the rough opening. Drive in any nails with a nail set and remove any debris that might be on the frame.
Spread a generous bead of caulking on the bottom sill.
Working from the outside, lift the new window into the opening and center it in the window frame.
Drive a nail partway through the nailing flange in the upper right hand corner to hold the window in place and use a level to get the window plumb and square. Use shims to hold the window in place.
Check from the inside that the window operates properly, and fasten the shims in place using 2 inch nails.
Finish nailing the window in place by nailing through the flange on the outside with 3 inch nails.
Install insulation (either spray foam or fiberglass) around the window in the gap between it and the window frame.
Install the trim boards on both the inside and the outside.