Take measurements of the width and height of the window opening from inside the tracks where the sashes are. Move the sashes up or down as needed to get at the sides. Order your new double-pane window with those measurements. Leave the old window in until the new unit arrives.
Remove the old windows by prying off the trim around the inner edge of the opening with a pry bar and hammer. Keep the trim intact as you remove it. Set it aside.
Pull the window sashes into the room, clearing the opening. Don't remove the border of trim that's around the outside edge of the window, between the window frame and the log exterior.
Set the replacement window unit in the opening. Set a level on one side of it. Slide shims around it, between the unit and the surrounding frame, until it reads level.
Drive wood screws through the holes in the sides of the unit, outward into the window frame, to secure the unit.
Press fiberglass insulation in and around the spaces at the perimeter of the window unit, filling and sealing the spaces.
Put the trim back in place around the window unit, using a trim nailer to affix it. The trim will hide the gaps and trap the window.
Caulk the lines where the trim meets the wall and window on the inside and outside.