Identify the central atom and the number of valence electrons it has. For XeF_4, the central atom is xenon (Xe), which has 8 valence electrons.
Count the total number of electrons around the central atom by adding the valence electrons of xenon and the electrons contributed by the four fluorine atoms. Each fluorine contributes 1 electron for bonding, so total bonding electrons are 4 pairs.
Determine the number of electron pairs around the central atom, including both bonding pairs and lone pairs. Xenon in XeF_4 has 4 bonding pairs (from the 4 fluorine atoms) and 2 lone pairs, making a total of 6 electron pairs.
Use the VSEPR (Valence Shell Electron Pair Repulsion) theory to predict the electron pair geometry. Six electron pairs arrange themselves in an octahedral geometry to minimize repulsion.
Consider the positions of the lone pairs. The two lone pairs occupy positions opposite each other to minimize repulsion, leaving the four fluorine atoms in a square planar arrangement around the xenon atom.