What is the correct way to apply choke at startup?
For some reason, there are some riders who think it's a badge of honor or something to "never have to use the choke". Well, it's a carbureted engine with a manual choke. You're going to have to use it most of the time when the bike is cold.
Choke is usually only needed to start a cold engine, but every bike varies. Starting after you've stopped for a while, when the engine is partially cooled down, might require some choke, but not as much as when you start it in the morning. Use the same 'gradual-on' method (see below) in this situation. It may take some practice to get your starting technique perfected.
To use the choke: On the 250, you pull the lever toward the rider to apply choke, then push it away to disengage. Turn ignition key to on position; leave choke off. Press starter button with one finger (no throttle) while gradually turning up the choke. After about three seconds, the choke and carb priming should be adequate to start the engine. Use no more choke than necessary to keep the bike idling. Idle speed at startup will most likely need to be slightly higher than when it's warmed up.
The gradual application method is better than just turning on the choke and then trying to start it, because the Ninja rarely needs full choke to get going. You don't want to give it too much choke, because you risk flooding the engine.
As soon as the engine runs without dying (from several seconds to no more than 60), ride off with the choke still on. Do not idle the engine to warm it up. Keep the revs low, and gradually lower and then turn off the choke when the bike can run fine without it. This may be a few blocks or a few miles. Increase revs as the bike warms up, and don't run it hard until it's fully warm. Make sure to check a couple minutes into the ride to make sure you're not riding around with the choke left on.
On the other hand
Some people have trouble with the gradual-on method. Here's a way you can try if you're not having much luck: Set the choke lever at about halfway, then hit the starter. Normally it will fire right up and the rpm will quickly jump up. Turn the choke up or down to keep the bike running, staying under 3000 rpm until you start moving. Ride off easily, closing the choke completely within a few blocks.
Remember that every bike is different, and you need to find the method that works best for you.