There's a shorter definition that could be made: "freestyle fashion". Even though this trend is supposed to be something you do without caring, it's mainly youthful and cute. When I first read about this, all that was going through my head was "I've been doing it for years then... ". I honestly think Japan is a bit strange (well, it always was) for making this a trend because you can't sell "Aomoji-kei" in a store. If you're dressing up without caring, it's hardly fashionable. If you are somehow nicely coordinated in "Aomoji-kei", you're defeating the purpose.
Basically if you're striving for "Aomoji-kei":
- Find mismatching clothes. Clashing prints or strange colour combinations will work (for example, gingham and floral or navy and neon pink)
- Get mismatching accessories (mixing up your metals, anything peculiar like a fly necklace, patterned head bow, etc)
- Go out and wear your outfit without caring about whether it matches or not. If you do check yourself once and decide to change, you're defeating the purpose!