It will be helpful to see the LED strip you have.
Which motherboard do you have?
Some motherboards have 4-pin LED connectors to plug LED strips.
Since you have a 2-pin strip you might need to use a male MOLEX connector.
If you have a male MOLEX connector lying around, solder or connect the pins to the positive and negative wires. The Yellow wire is 12V, and the black is ground.
You could use hot glue to cover and secure the wires so they don't come loose or keep them from touching anything else in the case.
Then plug into a female MOLEX connector from your power supply.