If you live near one of the airports, fly from that airport. Each of the London airports has regular flights to Amsterdam, the prices depend as much on when you buy as on the airline. Just remember to fly to Schiphol, (not Eindhoven, which is two hours and €27 or so away.)
If two London airports are both in easy reach, search which one has the cheaper flights on the days you want to travel. Do include the time and money it will take to get to and from the airport.
If you live near St Pancras or have a good connection to it, the Eurostar train is a good option. But if you have to travel across London with a few changes it will take a lot extra time.
It is fun to take the train but with the airport style check-in and security, the advantages of taking the train are smaller than with other trains.
There is the train-ferry-train (although temporarily train-ferry-bus-train) connection via Harwich and Hook of Holland. Very good if you travel overnight, less convenient if you travel by day as it takes quite a bit of time. If you live between London and the coast at Harwich you can usually take a train from near home, saving you having to travel to London to start your journey.
You can also use the same ferry with a car or use one of the Dover ferries or 'car train', which can be cheaper than flying or the train if you have a car full of people. Just remember to park outside Amsterdam, as parking there is expensive. Park and ride options are often a good deal.
Mostly cheapest, coach. Usually you start from London Victoria but there might be more departure points by now, and if you live farther from London you can take a coach to Victoria for an easy change.
The Amsterdam terminals are railway stations in the city region, with bus and often also Metro stations near, for a range of option to your Amsterdam location.