Phosphorus is in group 5 of the periodic table, meaning that it has 5 valance electrons. Each fluorine can donate one electron to the phosphorus. This means that 3 electrons are donated in total from the fluorine to the phosphorus as there are 3 fluorine atoms. This means that phosphorus has a total valance electron count of 8. Each of the fluorine atoms can ‘pair up’ with a phosphorus atom. This gives 3 bonding pairs and 1 lone pair of electrons.
The overall shape is trigonal pyramidal. A trigonal pyramidal shape can be imagined to be a tetrahedral shape where one of the bonds has been replaced with a lone pair of electrons. The bond angles in a trigonal pyramidal shape are slightly different than in a tetrahedral shape. As lone pairs of electrons are slightly more electron dense than bonding pairs there is more repulsion between the bonding pairs and the lone pairs than between 2 bonding pairs. Therefore, the P-F bonds are squeezed together slightly in a trigonal pyramidal shape, bringing the bond angle down to 107 degrees from 109.5 degrees in a tetrahedral structure.