To remove the piece I use 2 methods, firstly if it is a small piece and the back of it is not finished I use a parting tool, if however it is a large piece or I do not want to mark the back of the piece I use a hot air gun or hair drier. To remove using a hot air gun do not hold the gun too close otherwise you risk over heating and cracking the wood, hold it close enough to warm the glue and slowly turn the piece by hand until you can pull it free.
For larger items that are too big for the swing of my lathe I mount them differently.
First mount the glue chuck on a screw chuck or face plate and true it up, make the face slightly concave and bevel the edge then remove from the lathe.
Find the center of the piece you want to mount and draw a circle the same size as the glue chuck.
With the piece laying on a flat surface hold the glue chuck in place and put a dab of glue in 3 or 4 different places around the piece to hold it in position then after a couple of minutes when the glue has set enough mount on the lathe and fill in grove as above. After about 10 minutes the glue should have cooled enough to give a good grip and you can start turning. However if I am using this method I usually glue it up an hour or two before I want to turn it to make sure the glue has gone off completely.