If you are planning on adding a single color LED...
Turn off lights. Cut wires. Splice in an additional red/black wire for the new light with small wire nuts. Then run red and black thru cabinet to new light location and wire new light. It's a simple 2 wire connection.
You can buy an inline single color remote that will turn the cabinet light on/off and even dim it.... Get a controller and cut the plug end of the controller to expose the red and black wires and put the controller between the new LED strip and the new wire you spliced in.
If you want multicolor LEDs that will require a little more wiring at the end of the new wire that was added. This scenario has to have a controller. You would essentially do the same as above but once you bring down the red and black wire thru the cabinet, you will hook up to the controller as described above. The difference will be there are 4 wires between the multi color controller and the LEDs. Most controllers and multi color LEDs have a 4 PIB connection and you should just be able to plug it in. If not, you have to make 4 wire nut connections.
I suggest you look on www.hitlights.com
. They have a ton of installation videos to show you how to wire everything if you're not familiar with DC current. You can also call them and tell them what you are trying to do and they can make you a list. They are out of Baton Rouge,LA and I have had a really good experience with them. I've probably placed 5 or more orders thru the years.
Installing this is really very simple. You shouldn't have any problems.