Answer:
Once you reach the required level (usually a few over normal), go to "Trainer HQ" and Click on "My Pokemon".
There will be a link next to the Pokemon saying "Evolve Me" (next to the column which says whether its a shiny, metallic etc.). Click on that link.
Beware though because if you evolve something then the Pokemon pre-evolution will be removed from your pokedex (unless you have another one of the same Pokemon)
So if you evolve Pidgey into Pidgeotto, Pidgeotto would be added and Pidgey would be deleted as entries into the pokedex.