London to Amsterdam, Best Transportation

The cheapest way is by air. Most all the surrounding airports have direct flights. I prefer easyjet via Gatwick Airport. You can also do it by train, it takes a little bit longer, and is bit more expensive, but it's more comfortable and scenic. Take the Eurostar from St Pancras to Brussels (if you wish you can spen a few hours walking around Brussels). From Brussels to Amsterdam take the Thalys high-speed train. You can get cheap non-refundable tickets by booking well in advance at:

http://www.eurostar.com

and

http://www.thalys.com

Keep in mind that going by air you have to allow extra expense and time to get to/from the airports. The train goes from city center to city center.

There's also the "Rail and Sail" option offered by Stena Lines ferries...a package deal taking you from London's Liverpool St Station to Amsterdam's Centraal Station, via train and ferry. A great way to travel, especially if you book the overnight ferry, as it takes care of one nights accommodations. Check the Stena Lines website http://www.stenaline.co.uk/ferry/rail-and-sail/

There is both a cheaper and more flexible way to travel by train all the way than taking the Eurostar to Brussels and a Thalys train from there.

Instead, take the Eurostar to Brussels and an InterCity train from there. Book the whole route well in advance at NS Hispeed to get a discount fare as low as €50. Since no reservations are possible on IC trains (required on Thalys trains), you can stop over for several hours in Brussels and simply get on the next available train when you're ready to leave.

It's cheaper, but taking the IC train from Brussels to Amsterdam adds almost an hour to the journey time. Thalys now uses the new high-speed tracks between Brussels and Amsterdam; the IC trains still use the old tracks.

I vote for air, though circling while waiting for a spot to land usually makes it longer than stated (in my experience).

Bus is one option I would avoid for teens - cheap, but looooong trip.