How can I re-attach the jeans button?
Kirth: Denim is very hard to hand-sew through, especially through areas of reinforcement or seams, like the waistband of jeans (although, hmm, my jeans are kinda thin). The area where it fell out probably has a hole in it too now which you’d have to fix before sewing something through it. If the denim was thin, you could get a sturdy needle, reinforced thread, and a new button (one w/ a shank instead of holes). Patch the hole where it ripped out if necessary with self-adhesive patches (probably the new button will cover it up anyway and hold it in). Then stitch your new button in. Alternatively, you could buy a new jean button like you have, punch a new hole in your patch, then attach the button (it’ll have 2 parts and require clamping together). Hmm, I like junkbox’s idea.
(Or, inspired by 445supermag, you could liberate a normal button from another pair of pants. Then you only need a needle, thread, and toothpick to sew the button back on. Sandwich the toothpick between the button and where you want to reattach the button on the pants. Insert the needle through the side of the fabric not touching the button and bring it past the toothpick and up through an eyelet. Sew through the eyelets a whole bunch, past around the toothpick and through the fabric each time. Go up and through new eyelets each time. Once you get enough thread to keep the button in place, centered, and sturdy, slide the toothpick out. Again, bring the needle up through the pant, but this time don’t bring it through an eyelet.