To fit a fixed window, measure the opening and order a window of the appropriate size. Install the window frame using screws and sealant, ensuring it's level and square. Secure the glass in place with glazing beads or silicone.
There must be some wiggle area around the window in the aperture so that it may be shimmed and leveled. Take out 1/4 inch from the width and the height when placing an order for a replacement window. If the manufacturer suggests a larger clearance, you'll be glad you saved the original measurements.
To install double-glazed windows, window fitters remove the old window and measure the opening. They'll install a new frame, secure the double-glazed unit with glazing tape or silicone, and add insulation. Finally, they'll seal around the edges to prevent drafts or leaks.
Windows can usually be installed even if it's raining outside. However, there are some severe cases where it's much safer not to. When it's pouring outside, it's not safe to go out.