How do I put legs on a curved surface?

Get some thick stock, maybe a few heavy branches from the tree, and drill a 1.5" hole saw into the end of each leg about two inches deep. then with a regular saw, cut around the outside two inches from the end until the outer part falls out and you're left with a 1.5" round stud out the end of the leg. Then drill a 1.5" hole in the seat and insert the leg into the hole. You'll have to file the peg a bit to get it into the hole.

I'm assuming you don't have access to a wood turning lathe.

Log furniture is usually assembled using large hole saws and or Forstner bits. I have an adjustable bit that I can expand the cutter. Drill the holes then shape the legs to fit I found a strip sander quite handy for getting my legs and rail pieces to the correct size. I find the depth of the hole needs to be 1.5-2 x the diameter for chairs if the legs are not set deep enough they tear out. The other thing that I found out after making some furniture MAKE SURE IT IS DRY! I made some chairs out of trees we cut I trimmed everything assembled and a few months later it became very wobbly the legs dried and were smaller than the holes (gorilla glue saved me having to redo all the legs). If you look at log furniture you will see what I mean on cutting the ends down, I make the ends as tight as possible with out splitting the rail or seat. If the wood is well dried and the leg goes in 1.5 x the diameter only a small finish nail can be used just in case they start to losen up.

Traditionally, you want tapered holes and tapered legs inserted in the holes. Those holes should be bored at an outward angle, as well, not vertically. If things shrink, the leg just seats a bit further in the hole (if the hole is deep enough to allow that, of course.)

This may require tools you do not own, but they can be found.

For reasons of geometry, 3 is the magic number of legs to not wobble, and traditional for this sort of stool as a result.

Best to remove the bark, by the way - it may fall off later, and tends to harbor wood eating beetles.

There are tools made just for what you are trying to do. Maybe more than you want to spend, but wanted to show you anyway. Below is a screen shot of parts of it as well as a link. I have not used these personally, but I have heard they work well.

https://www.northerntool.com/shop/tools/product_200459372_200459372?cm_mmc=Google-pla&utm_source=Google_PLA&utm_medium=Power%20Tools%20%3E%20Drills%20%2B%20Accessories%20%3E%20Tenon%20Cutters%20%2B%20Kits&utm_campaign=Lumberjack%20Tools&utm_content=16804&gclid=CjwKCAjwmf_4BRABEiwAGhDfSWvXYEPazetB9Yl9tCK3GuJb8yTg9l3L5JsylUHSrUTY7lMAVqcSeRoCbM8QAvD_BwE