Newbie: how to wire panel to battery to appliance, litterally

I don't want to confuse you with a lot of talk about ohms law and electrical stuff, so I'll get right to the point.  You have an 11 watt panel that I assume is rated for 12 volts.  This tells me that the current flow from the panel to the charge controller will not exceed 1 amp.  To be on the safe side, the wire that you use from the panel to the charge controller should be no smaller than 18 guage.  18 guage wire can handle 2.3 amps, maximum.  Your single LED light draws much less than 1 amp, so you can also use 18 guage wire from the battery to the light.  However, it is important to point out that your battery is capable of putting out much more than 2.3 amps.  A short circuit could cause 18 guage wire to catch fire.  To avoid this, be sure to use fuses. For your application, you could use automotive fuses and fuse holders.  Be sure to install a fuse at one of the battery terminals.  Connect nothing else to this battery terminal.  In doing so, you are making sure that a short circuit anywhere in your wiring will not result in a fire.

The length of the wire is also an important consideration.  Wire has resistance, and you might need thicker wire to keep your voltage drop across that resistance to a minimum.  Here is a web page that might be helpful:   http://www.powerstream.com/Wire_Size.htm

John

Becky,
     John has most of the installation correct.  I would start here.  First install the panel facing south using a compass and tilted at about 45 degrees or so.  I would use a 3 wire 14 guage sunlight resistant extention cord (available at any harware store>HWS).  3 wire so you can use the green wire to ground the panel using a ground rod.  Use the black wire as your positive(+) and white as your negative(-). (most 12 volt systems are wired with black as - and red as +) so dont get them mixed up. Or to avoid any confusion you can us a red magic marker to color the white wire red and go back to the red + and black -.  Run the wire from the panel to the charge controller and hook it up as shown in the instructions from the controller and panel. Wire from the controller to the battery and install a 5 amp automotive fuse holder, (but do not put the fuse in untill you are done), to the + lead using a butt connector then to the battery using a ring tongue connector (available at a auto parts store). Hook up the - wire to the battery - post in the same manner (no fuse here). You will also need a crimping tool but they dont cost much and the counter man can help you pick out the right tool and connectors if you take the battery and wire with you).  Next run the wires to a "handi box" (HWS) using romex connectors for the wire entry and exit thru the box and put your switch in breaking the + wires at the switch. Next run to the light and hook up the + to + and the - to -.  I woud do away with the cig lighter plug in and wire it direct to the light using butt connectors. Put in a ground rod as close to the charge control as you can get using a hammer to drive it into the ground and run a # 6 bare solid copper wire from the rod lug to the controller and ground the panel and the controller to earth ground.>HWS Put the fuse into the holder and turn on the light switch. WOO HOO!!  If you need a wiring diagram or have any questions contact me at oltoby @ sbcglobal.net.
Jim C.