You need to remove the carbs. Once off, remove the bowls. Under the bowls in each carb there are 2 large cream colored floats connected to a small valve. Basically, when the bowls are full, the valves are closed. If the valves never close the carb will flood and overflow.
Might as well clean the whole carb since you have it out. When you take out the floats, be careful to no bend the little wires that operate the valve pin. Also, remember to replace all the carb screws with hex head while you have it out. If you do a quick search on youtube, there are some great videos for "ninja 250 carb cleaning". Newgen or pregen, the cleaning process is basically the same.
And I am sure @
Motofool will be here shortly with some great links to removal, cleaning and such. He is great for that.
But I am a video person myself.
Ask if you need or have any specific questions. I will be happy to help as best I can.