Explain the trends in electronegativity in the periodic table

As you go across the period from left to right (excluding noble gases), electronegativity increases. This is because the nuclear charge increases (Atomic Number/number of protons) and atomic radius decreases and therefore there is a larger nuclear attraction which bonds the electrons more strongly. Electron shielding remains similar so is outweighed by the other factors.
As you go down a group, the shells get larger which means there is greater electron shielding. The atomic radius increases so the nuclear attraction decreases. The nuclear charge is outweighed in this situation.