But I already have .1uF capacitors at each chip, and 10uF at all breadboards.
Well what ever you have is not enough, either in the terms of layout ( bread boards are bad ) or in how you have applied them. They need to be ceramic caps and they need to have short leads and they need to be as close to the chip as possible. You might try a star distribution arrangement, where the wire supplying power to each chip is connected to one point. I suspect you have them chained at the moment.
How can I, preferably step by step, decouple the noise I've got now?
Each situation is different, no one can give you a step by step guide, this is not cookery it is electronics. No amount of decoupling capacitors can rescue a bad layout. It is a matter of trying to understand what you are doing.
How about posting a photograph of your setup?