Just cut either straight down or at a slight angle with a shovel or whatever tool you feel works best between the mother and pup. Make sure you get enough roots with the pup and plant it at the same soil level in the ground or in a pot. Dont over water or fertilize until you see new growth and it should be just fine.

Josh

don't know how true it is but have heard to let it get at least 12 to 18" tall before cutting it, and once cut, leave in the pot for better chance to root without disturbance of the fine roots it may have, wait a couple of weeks then you can remove? hope i am some help

How do you keep the pups alive? I have a dwarf banana (kept indoors at all times) which has twice pupped, but the pups have died completely before getting to an inch or two high.

They need FULL SUN. ALOT of sun. Without it they wont die but they'll look pretty bad until they get out in the spring. Sounds like the pups dont get enough energy because the mother plant is struggling for light. If you dont have a good window for it, try some grow lights and a humidifier. At least get a humidifier.

I have separated a lot of pups this summer and have noticed the big ones (tall) have a lot more roots then smaller ones(which usually have none). Not sure if its even worth bothering with smaller pups, all of mine died or are in the process!