I'm making a lolita hat but need some help.
 

So I understood the main idea of how to do it and it looks great. The only problem is I need a way to attach it to my head. What do you guys think would be the best way, string or headband maybe? The thing is I tried just attaching a string to it but it is to heavy and wobbles a lot. I really want to be able to wear it!

if it wobbles then maybe the size is too big?
and what is the headband method?

Depending on the specific style you made, it is not uncommon to see some lolita hats that are tied on with sashes that can make nice bows under the chin and off to one side. The sashes(straps) can be wide enough to hold any hat in place if the size of the hat is balanced to the width of the strap.

I have seen them held in place with an elastic band, but unless it is tucked under the hair at the back of the head it seems to detract from the image. And if the wieght or size is significant an elstic band will not hold unless worn under the chin.