There are various options and you can check out public transport for specific times and journeys here
But to give you a rough idea let’s say you want to get to the West End to see a show or go out for a meal.
Cheapest: catch a bus. There are nightbuses (N89 from Trafalgar Square) all through the night so you don’t need to worry about getting back.
Quickest: catch the 89 bus to Blackheath Station then a train to Charing Cross
Easiest: take a cab.