There are 2 main techniques for double eyelid surgery. They are divided into stitching and cutting techniques.
Stitching techniques make use of minimally invasive procedure to secure the eyelid skin to the tarsal plate, hence creating a crease in the skin.
Cutting techniques rely on fat, muscle and skin removal in order to create an anatomical defect which causes the eyelid fold to become more apparent.
In addition, there is a common misconception about whether fats should be removed from around the eye during the course of the operation. This is not a hard and fast rule, and less is not always better. Your doctor should examine you before advising.
There is no right or wrong. Each procedure is recommended for a different set of patients. Only a consultation with an experienced doctor will be able to tell you which is the procedure most suited for you.
Warning: some doctors perform or are trained in only one technique of creating double eyelids. It is advisable that you see a doctor who is comfortable with both techniques.