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

Tetrahedral is the form of ${\mathrm{BF}}_4^{-}$'s molecular structure.
Each of the four flourides adds one electron to the covalent bond, and as boron has three valence electrons, each covalent bond. The molecule's overall negative charge provides another electron.
Overall, we therefore have 8 electrons (3+4+1). The picture above represents ${\mathrm{BF}}_4^{-}$.