The tan piece in picture 1 is the socket. You removed it when you untwisted the bulb, and it is still on your old bulb. Pull it off and insert your new bulb into it. Then twist it back on.

If you lost it, go here:
http://www.superbrightleds.com/cgi-b...0_sockets.html

Get the T10S-TW Twist Locks for $1.19 a piece.