Start assembling everything into the ring base by putting a dot of hot glue down where the switch rests. You should be able to push the switch into this recess, feeling just a bit of friction as it goes in.
Next, place the Trinket face down so that the small plastic pin protruding up from the center of the ring base fits into the screw hole of the trinket. The wires from the battery should slip into the little notch next to the switch.
To keep everything together, use a tiny dot of hot glue to hold the LiPo to the Trinket.