The phrase "ura uchi" literally translates as "back strike". Although it can be used as an opening move in a combat or kumite situation, in my experience, it's only likely to succeed as part of a combination, or more probably as counter following a block, particularly soto uke. Although it doesn't have a lot of weight behind it, it can be effective in interrupting an aggressive attacker and turning their stance from offensive to defensive. This can give you time to follow with more powerful strikes. Unlike many strikes which can be targeted at many parts of the body, a true ura uchi is suitable only for attacking an opponent's nose. You could attack the top of their forehead as a last resort, but you risk getting hurt as much as your attacker.
This one of the easiest strikes to perform. In line drills, you should start with both fists raised in front of you at about jaw height. Your fists should be clenched and your palms should be facing each other. Tuck your elbows in so that your ribs are protected.
Now simply extend your fists towards your opponent's forehead, straightening your arm in the process. This is one the few techniques where rotation occurs at the start of the move, rather than the end. As soon as you start to extend your hand, twist your wrist so that your knuckles are facing towards your opponent. As your fist reaches its destination, relax your wrist and whip your fist downwards so that your knuckles strike your opponent's nose on the bridge, where it joins their face. Quickly whip your hand and arm back towards you to end up where you started.
In a fight situation, you'll probably have your arms up in a guard, with one hand in front of the other. Although for the sake of exercise, you might practice striking with the rear hand, in reality you're likely to use the lead hand, which may well have just performed a block.