What is the geometry of the fluorine atoms around the boron atom in ${{\mathrm{BF}}_4}^{-}$ ? 

The molecular geometry shape of ^​${\mathrm{BF}}_4^{-}$ , tetrahedral.

Boron has 3 valance electrons and each of the four fluorides contributes one electron to each covalent bond. The overall negative charge of the molecule contributes another electron.