How can remove this window screen to repair it?
This is a pretty standard screen repair. You need to remove the spline to get the screen out, which can be done with an awl or a narrow flat-head screwdriver.



You'll need a new screen, spline, a spline install tool (under $10), and a sharp utility knife.

It's not very dificult, but does take some patience. 



It looks like this is a fixed window, so you'd have to install in place. 



Position the new screen, and then push the spline into the channel, pulling the screen tight as you go. I'd start with the top edge. 

It's critical to get the first edge straight. Start with enough spline sticking out so you can wrap it down both sides, and on one side, also run back along the bottom. 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). 

Work your way down both sides at the same time, keeping it tight as you go, then finally install the bottom edge.

Finally, cut the excess screen off using the knife.





Here's a full guide (and the source of these pictures): http://www.familyhandyman.com/windows/repair/how-to-fix-a-window-screen/view-all