Catch a Southern train from East Croydon to Victoria then a 24 bus to Leicester Square or the Underground from Victoria (Victoria Line to Green Park then Piccadilly Line to Leicester Square). If you're travelling after 09-30am weekdays or anytime wekends buy a Zone 1-6
travelcard.
An Alternative route is to catch a First Capital Connect train to London Bridge then change to a South Eastern train to Charing Cross, which is 5 minutes walk from Leicester Square,
All these services run very frequently