How you approach an intersection matters as much as the give-way rules themselves. Slow down early, work through a routine so nothing is missed, and know which control beats which.
Approach in a routine
Don't speed up as you approach when another vehicle is near or crossing the intersection. A useful routine is CMSBGA: Course (pick a safe, legal path), Mirrors (check behind and your blind spots), Signal (at least 3 seconds if turning), Brakes (slow enough to give way), Gears (change if needed), then Accelerate back to traffic speed once it's safe.
The give-way rules in short
At stop signs, give-way signs or traffic signals, stop or give way as required. If you're turning — including leaving the path of a marked centre line, which counts as turning — give way to vehicles that aren't turning. Turning right, give way to all oncoming vehicles, including those turning left. At a T-intersection or driveway, traffic on the road that ends (the bottom of the T) gives way to traffic on the road that continues. For anything else — a roundabout, or a crossroad whose signals have failed and are flashing yellow all round — give way to everything coming from your right. Where two oncoming vehicles are both turning right, neither has to give way, but watch for straight-through traffic hidden behind the turning vehicle and give big trucks and buses extra room. A police officer directing traffic overrules all of this.
Stop signs
At a stop sign you must come to a complete stop — not just slow down — where you can see all directions, marked by "STOP" and a single yellow line on the road. Stay stopped until you've given way to every vehicle, including cycles and motorcycles, and don't go until it's safe. If you and another vehicle both face stop signs, fall back on the give-way rules.
Give-way signs, and which control wins
At a give-way sign, slow down and be ready to stop, give way to all other vehicles except those facing a stop sign, and don't go until it's safe. If you and another driver both face give-way signs, use the give-way rules. And where one vehicle faces a stop sign and the other a give-way sign, the vehicle at the stop sign gives way to the one at the give-way sign.