Red light on BNC

Here is the colour code and there meaning of 3+1 cable support Analog and Analog HD Cameras
Red Wire = Volt +
Black = Volt -
yellow = Video
White = Video ground

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Question edited for Capitalization and funky punctuation.

Makes and models are useful in such questions.

Best guesses;

red to red (power)
yellow to yellow (signal)
aluminum to copper (earth / shielding)
black to white (both are designated returns / negatives)

videos and articles

https://www.google.com/search?q=how+to+connect+bnc+connector+to+cctv+camera

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Samsung security cameras are proprietary so you have to get another Samsung DVR .

Red lights on means : Camera getting power.
No Video Means: your connection or BNC Connector is bad or not connected properly.

CCTV Networking Technical Support

Why would you use composite video? It's very low end., subject to interference. Change to HDMI.

New Samsung HDTVs use the GREEN RCA input for the yellow RCA video cable, plug it in there. Select the AV input on the TV. For sound, connect white RCA cable to white RCA input on TV.

The cable should be labeled with R (RED video signal), G (GREEN video signal), B (BLUE video signal), V (Vertical Sync signal), and H (Horizontal Sync signal), so you just have to match the plug to the sockets.
I hope it is clear explanations.

the tv has as follows. Use the bnc conectors to hook it to the RGB & R and L Audio. or reg Comp input ( Yellow ,Red White.) can get adaptors at the Shack. Inputs
Composite BNC Back Composite RCA Back Component 3 BNCs Back RGB 5 BNCs Back RGB 15-Pin Dsub Back RS232 DB-9 Dsub Back

Only red(+) Black(-) and Yellow (Video) is used if you just cut off that mini din plug end and were looking at the wires coming from camera. I bought some standard power and bnc pigtails from DX.com and replaced that mini din cable they use to make their connections to a standard cctv type.
Un-screw the main lens cover and you will see a screw ring and by taking a verner caliper to catch on both sides you can unscrew camera unit ring and when you look inside the only wires you need to solder to new pigtail is red/black/yellow each to their own color.
Pushing the pigtail thru may be a little pain but with a little spit on wire makes it a lot easy.
Re-assemble in reverse and you should be up and running.
Camera runs on 12 volt with center of plug positive and video bnc center is video.
Hope this helps.

The internal antenna BNC connection (the little steel bayonet that the secures the antenna or extender cable) is a common failure on these units. The threaded retaining ring on the outside of the antenna BNC comes loose when installing/removing the antenna connection, and eventually the BNC rotates and the solder joint inside fails. This happened on mine recently, if you are handy fixing small mechanical parts and a good solderer it is pretty  easy to fix. Remove the batteries, remove all six outer case screws (but not the one with the oval metal plate) and gently pull the housing apart. Check the solder connection of the coax wire to the BNC pin & shield. If it's broken and the BNC is loose in the GPS case, tighten the outer BNC retaining ring VERY tight, add a drop of thin super glue (Hot Stuff or Permabond CyA, etc) to keep the ring/BNC/case mated, then repair the coax solder  connection. Replace all the screws and test it outside. If it's an aviation GPS you would of course have this done by an FAA licensed avionics specialist. Wink wink.