What's the best way to shore up the bottom of a drawer?

https://www.thisoldhouse.com/more/support-sagging-drawers

Not sure what your drawer is made of but I used pieces of a broken yard stick with small nails to help stabilize my cutlery drawer in the kitchen.

If you can slide it out, you can often flip it over. Some drawer bottoms are super flimsy. I did this with a dresser, and ran duct tape in a cross pattern on the bottom to make it more rigid

I’m guessing either the bottom of your drawer isn’t going into a groove into the drawer side or it has broken off? Whichever it may be, your best choice is to turn the drawer up side down and take a drill to drill small pilot holes and screw in some Sheetrock screws at least 1 1/4” - 1 1/2” long number 10 screws. Color your choice, they come in gold and black usually! When you drill your pilot ones you want them very small so your screws have plenty of wood for the threads to grab in the wood and don’t strip out! A 1/16” bit should be fine or you can take a nail too and cut the head off the nail and put the headless side in the drill with the point of the nail showing. Then use the nail just like a drill bit! It will go right into the wood with a little pressure with your drill running! Try to make sure your screws go pretty straight down into your drawer side so it don’t come out the sides of your drawer. if you can get some glue between the bottom and your sides this would also make it stronger. But the screens themselves should be enough if spaced roughly a inch apart It should be plenty strong! Good luck

I’m a Cabinet maker/ jack of all trades type guy, there’s not much with houses I haven’t done. When it comes to woodwork though. I can make pretty much anything Or fix it when necessary! Always have someone showing up with a broken door or drawer they need fixed. So you could say I’ve dealt with this problem a few times. Just never for my own stuff. In 25 years I’ve never yet had anything I made come back broken yet! My drawers are built to hold at least 100lbs. So you got to work harder to break them! LOL