What is vsepr theory based on?

The theory is based on the idea that electrons repel each other and try to get as far apart from each other as possible.
You can read an excellent summary of the theory at
http://www.nyu.edu/classes/tuckerman/adv.chem/lectures/lecture_11/node9.html
Once you have drawn the Lewis structure for a molecule, you can determine the steric number of the central atom.
You can then use the assignment table in the article to determine the geometry of the molecule.
Example
Determine the of XeF₂.
Solution
The Lewis structure of XeF₂ is
We see that XeF₂ has SN = 5: three lone pairs and two Xe-F bonds.
The assignment table shows that a structure with two bonds and three lone pairs is linear. So XeF₂ has a linear geometry with a bond angle of 180°.