How do keep a curtain rod from falling off the wall. g

Use screw in wall anchors.

There are little helpers called Stud Finders. They are inexpensive and found at the hardware department of big box stores.

If your home is built to code, studs should be 16” apart. You could start at the corner, measure and mark each 16” , then rap around the area listening for a difference in the sound. the drywall without a stud should have a more hollow sound when rapped. Once you‘ve Found where you think the stud may be, try a test hole to confirm. Barring that, you could get heavy duty wall anchors for your curtain rod

Watch a few YouTube videos to solve your problem: https://www.youtube.com/results?search_query=how+to+hang+a+curtain+rod