How Lithium Polymer Batteries are Made
Nate 
Forming and Electrolyte
In a separate room, the housing is made.
These machines cut, form, and create the slightly flexible but protective housing for the inner electrodes and electrolyte polymer. I believe this material is a type of plastic or PVC.
The electrodes are then inserted between the protective housing and thermally welded together on three sides. The fourth side is left open for squirting in the electrolyte.
Electrodes in their housing.
In a carefully controlled environment the electrolyte is pumped into the cell. This part of the manufacturing floor is tightly controlled for humidity and temperature. The fume chamber is even more carefully controlled.
Multiple lines going at the same time. The final step of this line is thermally welding the fourth side of the battery to contain the electrolyte and seal the battery.