Stop in a safe place, clear of the traffic lanes, preferably in a lay-by or parking area.
Before you lock your car make sure you have a key in your hand, don't just push the lock buttons and shut the door.
Before leaving your car, make sure it is safe and secure. Check the headlights are off, valuable personal items are hidden from view or locked away from opportunist thieves, the car is safely parked and wheels turned to the curb if on a slope. Note where it is parked if in a parking lot or unfamiliar area, and check the parking time limits too.
Try to get to the hard shoulder or safety zone before the vehicle stops.
If you have a flat tire, consider travelling very slowly to a lay-by or side road if there is no room to stop or the shoulder is not level.
Turn on the hazard warning lights - if fitted.
Turn off the engine and apply the hand brake.
Warn other traffic that you have broken down. Check the local road rules for the acceptable ways to do this. Raising the engine hood is one way.
Stay by your vehicle, but get out on the side away from the traffic.
Call for help - use a cell phone to call the police or traffic authorities and local autombile breakdown service if you cannot fix the problem yourself.
Many countries require you to have a warning triangle to use in case you break down. Its not always a requirement but definitely always a good idea. Leave it at least 50 meters (others recommend 35 yards) behind your car if you break down; on freeways about 100 m are better. It will prevent you being rear-ended if you have to stop in an unsafe location. A tow-rope and jumper cables are also handy.
Check with both consulates of the countries you are crossing: there may be special requirements when crossing by car, for example driving from Hong Kong to mainland China requires a change of number plates at the border and a PRC issued driving license, Argentina does not permit rental cars to leave the country, some nations require a Carnet de Passage. In some cases, crossing borders will require you to change the side of the road you drive on (eg. Hong Kong/mainland China, Thailand/Laos).