Ruud UAKB-018JAZ outside condensing unit will not run

Trace the wires (small cable) going to the out door unit. This is your 24v control circuit. when it enters the outdoor unit it ties to wires routing through the inside of the unit trace these down. For AC units 1 usually goes directly to the "contactor" (the item you push in and the unit runs?) the other wire can also go to the other side of this same item. But I suspect it goes through other tings before it finally gets there.
Some items are the high and low pressure switches and a delay timer.
A red button sticking out where you can reset it is the high pressure switch and if it clicks and lets it come on you may have a dirty outdoor coil or a fan motor outdoor that is not operating all time.
A low pressure switch has no reset normally on AC or HP.
A delay timer will have 2 3 or 4 wires depending on the type of timer. 1 of these wires goes to the contactor (usually) and one of them feed this wire. remove the wire going to the contactor. now 1 at a time take the other timer wires and touch them to the wire just removed. if the times is bad the contactor will click when you touch one of them with the removed wire.

If its a heat pump you will have to make the contactor try to come on around the board. and this you will need some knowledge on which and what feeds your contactor. Here Id suggest a technician. If I had a way to see your setup and wiring I could talk you through this but its too hard to type and would take way too long.