To get from the Eurostar to Stansted Airport, you can take a combination of the London Underground (tube) and a train or bus. The options are detailed below.
Underground and Train from the Eurostar to Stansted Airport
From the Eurostar platform, go to the London Underground in St Pancras station. Take the Circle, Hammersmith & City, or Metropolitan line from St Pancras to Liverpool Street station. The trip will take 8 or 9 minutes. Tube tickets cost less than £2 if you get an Oyster Card at St Pancras.
From Liverpool Street station there are trains to Stansted Airport. The train from London to Stansted is called the Stansted Express. It takes takes 45 minutes to get from Liverpool Street station to Stansted on this train.
Stansted Express train tickets cost £22.50 for singles and £31.50 for return in express class and £36.00 for singles and £51.90 for return in first class if you make a booking online.
Underground and Bus from the Eurostar to Stansted Airport
Buses and coaches from London to Stansted operate from Liverpool Street, Victoria, and Baker Street. Terravision and National Express operate from Victoria and Liverpool Street, and easyBus operate from Baker Street.
From the Eurostar, you will need to take the tube to either Liverpool Street, Victoria, or Baker Street. Liverpool Street takes 8 or 9 minutes on the Circle, Hammersmith & City, or Metropolitan line, Victoria takes 9 minutes on the Victoria line, and Baker Street takes 5 to 7 minutes on the Circle, Hammersmith & City, or Metropolitan line. All journeys cost £2 if you get an Oyster Card.
From the stations, you can choose which bus to take. There are a variety of options and prices, all of which are detailed here. easyBus tends to be the cheapest if you book online and travel at off-peak times.