Over memorial day weekend my tenants said they had about a half gallon of water drip through their ceiling. In the pictures below, the water is coming in the corner of the house in the bottom right corner. I was out of town and didn't see anything myself, but there was some heavy wind/rain when it happened. We've had light rain since then and haven't had more leaks.
I just got back and took a look on the roof and saw no popped nails, loose/missing shingles, etc near where the drip actually came in. However, as seen in the picture below, there was some flashing curled up with nails that had rusted and popped out of place. This is under a dormer window, so it is mostly protected with an overhanging roof. The wind likely just blew some water sideways across the roof and under the flashing.
The roof itself isn't in great shape, but I was still hoping to get a few more years out of it. This would be my first roof repair and I'm a bit lost on how to fix this leak. Should I get new flashing and simply slide it under the existing flashing? Should I use nails or screws? Should I just re-use the existing flashing and get some slightly wider nails and slap a whole ton of roof cement pretty much everywhere?
I've got some conflicting info on how to go about the repair and it seems simple but I'm worried about screwing it up as it is the tenants house so I wouldn't know immediately if it was just a small leak and I would also prefer not to bother them over and over while i attempt multiple fixes. Any help would be appreciated!
EDIT: Couldn't figure out how to attach the image properly, so see them here:
https://imgur.com/a/p9kxzMl