An object or job can be done neatly if everything is tidy and organized.
When people talk about doing things neatly, they usually mean getting them spotless and in order. Imagine cleaning your room after a messy week of school - you'd try to put away clothes, books, and toys so that it's all neat and easy to find. The same goes for organizing files on your computer or writing down notes in a notebook: if everything is tidy and has its place, then you can say the task was done neatly.
In a neat manner.
