I have searched the internet and this forum and maybe I am not wording it right, but I can't find an answer. Is there a way to leave carpet in place when staining wood floors that meet up to it. I don't have any transition strips exactly, more of a rounded edge on my wood flooring that transitions down to the carpet. Large putty knife? Wouldn't the stain get on the carpet after you remove it? Is there a way to tape it? Or should I just pull it off the tack strips and rent a carpet stretcher later?

Also any tips on sanding these rounded transitions.

You could try to mask off the carpet with regular masking tape. Press the tape into the carpet carefully with the top edge of the tape at the tip of the carpet fibers, then
press the tape so it goes deep into the pile between the wood and carpet. Use an almost dry bristle brush to spread the stain, working it into the grain. Then use a clean T-shirt rag to wipe off any excess. You will need to be careful.
Or you could just remove the carpet from the gully that it is compressed into between the tack strip and the wood flooring. Do not remove the tack strip. You will need to hold the carpet away with a strip of wood cause it will want to droop over the fresh stained flooring. After easing the edge of the flooring, careful the tack strip can poke you, and finishing the floor, you can re-install the carpet with a knee kicker, pressing the carpet into the gully with a dull screwdriver or cold chisel.