You should end up with a single piece of spline with the ends in one corner (though this isn't crtical, and if you have to cut it that's fine).
Start with enough spline sticking out so you can wrap it down both sides, and on one side, also run back along the bottom. It's critical to get the first edge straight. Position the new screen, and then push the spline into the channel, pulling the screen tight as you go. It looks like this is a fixed window, so you'd have to install in place. It's not very dificult, but does take some patience.
You'll need a new screen, spline, a spline install tool (under $10), and a sharp utility knife. You need to remove the spline to get the screen out, which can be done with an awl or a narrow flat-head screwdriver.
