Br atom has 7 valence electrons. As BrF₄⁺ ion carries one positive charge, the central Br atom would have 7 - 1 = 6 valence electrons, i.e. 4 Br-F bonds and 1 lone pair of electrons.
The shape of BF₄⁺ ion is shown below :
https://c1.staticflickr.com/9/8130/29416025263_9041015c67_o.png
The shape of BF₄⁺ ion may be described as distorted triangular bipyramidal or seesaw.