I'd like to add some under cabinet lights to a switch that is already there. It controls the light above the sink but is part of a circuit that has a switch which controls an outdoor light and an outlet.

Please advise. How do I get the under counter lights into the circuit? I'd like the above sink light and under counter lights to go on at the same time.

You will have to figure a way to get the hot switch lead to a thin box mounted under the counter. An easier way would be to get a touch switch and plug them into a counter outlet.

You may have to tap into the light (the one that you want to be on at the same time as the new one) or at least into the conductors that go to the light. In most cases, there is no neutral in a switch box, but there are exceptons.
If this is a standard switch and has only two wires in the box the switch is mounted on-there is no neutral