Don't ride up close to the vehicle in front, either overtake it or stay back and keep with the traffic flow. If you're too close to the vehicle ahead and it brakes hard then first of all you have to react (1/2 sec or 1 sec if you're talking to girlfriend). Next you panic grab the brakes because you're nearly on top of the other vehicle and this makes them skid especially on a non perfect surface. Being further back also allows you to see what's in front of the vehicle ahead and it also stops the driver in front from feeling intimidated.
Position yourself approximately where the driver of a car would sit in the road. This allows the driver to easily see you in his mirrors but it also gives you an easy route to overtake him when the opportunity arises. If you leave a reasonable gap then this actually makes it easier to overtake as you can use the space in front to accelerate when gaps in oncoming traffic appear. This same positioning comes in useful if you haven't got the space to brake and need more space.
Covering the brakes is easy to do on scooters. This cuts down the reaction and thinking time. If something looks iffy up front (a car fast approaching a junction etc) then change your position in the road, lay off the throttle and be prepared to brake.
When first applying the brakes be gentle and then increase to whatever is needed. Applying the brakes gently to start with (if only for a fraction of a second) settles the suspension and enlarges the tyres contact patch with the road - this means you can then apply much more break without skidding.
Brake ratios between the front to rear should almost be the same on most scooters as they tend to have the weight low down and evenly spread between the wheels. Rear brakes also tend to be softer than the front brakes on many bikes. This just means you can probably apply almost the same braking force to both brake levers. This also makes it easier to apply as you don't have to think too much. If you're carrying a passenger then you can apply more rear brake than usual.
Skids happen if you apply too much brake to one wheel. If you find the rear brake skidding then don't panic - just release the brake for that wheel and then re-apply. If the front wheel skids then it's very very easy to fall off unless you release the brakes instantly. In either case, if you end up skidding, then you were either riding too fast or too close to other traffic.
When to brake? This seems obvious but plenty of riders end up panic braking in the middle of corners or as cars pull out in front of them at busy intersections. It they just adjusted their speed in advance, either by braking or preferably just rolling off the throttle, their ride would be much more relaxing.
Bad surfaces like wet roads and roads covered in leaves mean you need to brake much more carefully to avoid skidding - this doesn't mean you can't brake fully but just be more careful in applying your brakes. Be particularly careful if it's started to rain after a long dry spell as oil builds up on the road. On gravel, in torrential rain and in snow (if you're very brave) you must ride much slower and only use rear brake. Braking distances also increase if you're carrying a passenger.
Traffic lights should be approached moderately. Adjust your speed so you don't race up to them in a mad rush and then end up sitting there waiting for the lights to change. Look further ahead and plan to arrive just in time for the lights to change. Always be prepared for people to dart out between the traffic at these points. Try to stop at the lights by just using the rear brake in the last moments of braking as this will make your stops much more gentle and controlled. If you carry a passenger this will stop them from bashing helmets with you as well.
Target fixation is when something is in the road in front of you and you hit it because you're staring so hard at it. Bikes tend to go where you're looking so look at the escape route instead.
Brake in a straight line because if you're trying to swerve and brake then the front tyre will just get overloaded and skid which will soon be followed by a fall. There's nothing wrong with swerving round an object and then braking when you're upright again. There's nothing wrong with just swerving.
Anticipate issues by looking at everything around you. Plan what's likely to happen and adjust your position and pace to suit. Practise on your ride to and from work by awarding yourself 2 points every time you see an issue before it actually happens (issues for another bikes count as well). Putting your feet down at traffic lights means deducting a point. Crossing without stopping gets a point. Every time you have to jam on the brakes or swerve then deduct 10 marks. How many points can you get in city driving?
Practise braking in a safe environment. Guess how much distance you need to stop at a certain speed - then actually try it out. Can you brake harder? If the front starts to skid then release it immediately. The typical T-bone accident happens because the car doesn't see you (your bad positioning), you didn't anticipate what was going to happen (your poor attention) and you either didn't brake as hard as your bike was capable (you never practised) or you jammed the brakes on too quickly and overloaded the front tyre.
If you know you're going to crash then try not to hit any static objects (lampposts, trees etc) and definitely avoid vehicles coming in the other direction. Just before impact straighten your legs and get off the saddle as it's best to get thrown clear rather than getting tangled up in the wreckage. If you have a choice of vehicles to hit then hit the one causing the accident as it will make the claim easier. Don't get up in a rage, remember accidents will happen but more importantly it will scare off any potential witnesses who might be able to help you in a claim. Always check the other drivers car for a valid tax disk (UK), if it doesn't have this then chances are they don't have insurance either so quietly ring the police and wait for them to come.