WHY? Stain a cheap basket...sale this one to buy several cheap baskets. Once you alter this basket it will be worthless.
Sorry.
Use a water based wipe on stain for this kind of project for the best results.

ginger

Ginger is right, if you are staining a real Longaberger basket - you will destroy any value of it and some are worth some $$$ now.

If that isn't of any importance - and you want the basket stained - I would not use a waterbased stain - but a oil based stain. I have stained baskets many times and just use regular oil based stain. Use a foam brush and do both the inside and outside, using a generous amount. It should stain evenly...just wipe off the excess with an old towel.

It will be messy and smelly. Do this outside if possible and let the basket dry in a garage or such if you can for several days.

I have several Longaberger baskets, and I use them all the time. I don't keep them as a collector item, but use them as intended. When they get dirty, I wash them using a gentle stream of warm water and a small amount of soap. I towel dry them and set them outside to dry on my porch. They are very durable.

I wouldn't stain something that's worth a lot either. But that's up to you. If you want to do it, I recently stained a basket and used Gel Stain. It won't run like regular stains and that made it nice! I didn't have stain all over the place!

GL!

Leslie