The rule in short
If no signs or markings say otherwise, vehicles from the right have priority. Applies at every unsigned intersection.
When it applies, when it does NOT, and the most common trap on the theory exam.


If no signs or markings say otherwise, vehicles from the right have priority. Applies at every unsigned intersection.
The right-hand rule is the fallback. It applies only when nothing else decides the junction. These do, and this is the order they rank in: 1. A police officer's directions, over everything, signals included. 2. Traffic signals, over signs. 3. Signs. Give way, stop, priority road. 4. Road markings. Separately, and whatever the above says: give way to emergency vehicles using blue lights and siren, and remember that trams have priority. If none of this applies, the right-hand rule decides.
You're driving in a residential area. The intersection has no signs, the right-of-way rule (right priority) applies to everyone. A car approaches from your right. Another car comes from the opposite direction, signaling left to turn in front of you. Order, per the right-priority rule: 1. The car from the right goes first. It's on your right side. 2. You go next. You have priority over the car turning left toward you. 3. The car turning left goes last. It must yield to traffic from the right and to oncoming through traffic. The right-priority rule governs the entire situation: traffic from the right goes first, and through traffic goes before a left turn from the opposite direction. No other rule is needed here.
Just because the right-hand rule is on your side doesn't mean it's SAFE to proceed. If the car from the right clearly isn't stopping (too fast, distracted, not signalling), yield anyway. Being right doesn't save your life.