Most curtain rods are going to mount to the wall above or on either side of the window trim. Here is a simple step-by-step instruction on hanging a standard iron curtain rod.   

1. Measure the length of the rod and the length of the curtains you are planning to hang
2. Holding the curtain rod brackets in place mark the screw holes on each side of the window in the appropriate spot.  For longer rods you may have hangers in the middle which can be marked after you install the 2 outer  supports and temporarily install the rod.  
3. Install the brackets with  wood screws and a battery powered screw driver if you have studs or framing lumber up to about 4”  horizontally from the inside of the window.
4. Fasten the brackets using screw in wall anchors if there are no studs in the wall.  

photo credit: gurms