I’ve done a little bit of embroidery on gloves, but mine were fleece. I don’t think cotton would be that different. Here’s what I did:
Open the seam on the pinkie finger side of the glove (most gloves have a seam there). Hoop a piece of sheer mesh cut-away stabilizer that has been sprayed with temporary spray adhesive. Open out the glove as much as possible and press onto the stabilizer, pinning or basting the parts left flopping to the stabilizer (away from the path of the needle) as securely as you can. Depending on your design, slip any additional stabilizer under the hoop after the hoop has been put into the machine. When I need to use additional stabilizer with sheer mesh, I like to use a very soft tear-away, nothing stiff or scratchy.
Before you begin you will want to mark the design position on the glove with crossed centering lines that will coincide with the centering marks on the hoop and plastic placement grid that comes with the hoop. Printing a paper template of the design makes positioning a lot easier!
When you are finished, sew the side seam back up.
A Bit of Stitch