Edinburgh is the capital of Scotland (UK) and a major financial and tourist hub. From Amsterdam it is some 660km away over the North Sea.
Here is an overview of the various travel options between the 2 cities - we will consider air, rail, coach and ferry...
1. Amsterdam-Edinburgh by Air
Flying is the easiest and most convenient travel option between the 2 cities. Scheduled flight time between Amsterdam Schiphol (AMS) and Edinburgh Airport (EDI) is around 1 hour 30 minutes.
Dutch airline KLM (Skyteam) flies up to 5x daily using a mix of Boeing 737s (KLM) and Fokker 70s (KLM Cityhopper). The cheapest return flights start at around €100 from Amsterdam or £80 from Edinburgh.
No frills airline Easyjet flies daily between Amsterdam and Edinburgh - expect to pay similar return fares to KLM when you include checked luggage and fees. Note, if booking a one-way flight only then Easyjet will be cheaper as KLM charges the full-fare for a one-way.
2. Amsterdam-Edinburgh by Train
It is possible to travel from Amsterdam to Edinburgh by train in about 10 hours.
From Amsterdam the journey has 3 components - travelling Amsterdam to Brussels Zuid/Midi by Thalys, taking a Eurostar train from Brussels Zuid/Midi to London St Pancras and then taking a UK domestic train from nearby London Kings Cross to Edinburgh.
See here for more info about travel from Amsterdam to London and Amsterdam to Brussels. You would need to purchase separate tickets for this trip - expect to pay from €59 for travel from Amsterdam to London.
Virgin Trains East Coast operate regular direct rail services from London Kings Cross to Edinburgh and this journey takes around 4 hours 20 minutes, stopping in Newcastle, York and a few other towns. There are a huge variety of rail fares in the UK so you could pay as little as £25 for a standard class single (if booking well in advance) right up to £140.
First class singles start from £55 one way - a hot meal and drinks are served at your seat.
Now whether you would do the entire Amsterdam-Edinburgh rail journey in one go is up to you - it would probably be prudent to add a stopover in London to minimise risk of missing the connection.
3. Amsterdam-Edinburgh by Coach
It is also possible to do the journey by coach via London although it will be a long-haul. Eurolines operate a 4x daily coach service from Amsterdam Duivendrecht to London Victoria - 2 by day and 2 overnight services - this trip takes about 11 hours. Partner National Express can take you between London Victoria and Edinburgh with a journey time of 9 hours for direct services.
Booking a through-fare will be around £50 single. You could split the ticket via London to see if cheaper fun fares are available.
Megabus also offers coach trips between Amsterdam and Edinburgh. It's possible to buy through-tickets with a change of bus at London Victoria. The journey takes around 24 hours. One-way fares are available for around €32/£25 if booking in advance.
Obviously you could also consider a rail-coach combination - such as coach from Amsterdam to London then a train up to Edinburgh.
4. Amsterdam-Edinburgh by Ferry/Train
Every night a DFDS Seaways ferry runs between Amsterdam Ijmuiden and Newcastle North Shields. This trip takes about 15 hours. At North Shields port take the bus to Newcastle station. From there you could travel on an East Coast train up to Edinburgh - this takes about 90 minutes and singles start at £9.