Frankfurt in Germany is one of Europe's major financial hubs and is located approximately 350km south-east from Amsterdam. Netherlands and Germany are both in the Schengen zone so passport controls are not necessary.
There are various travel options between the 2 cities - train, air and coach (bus)...
1. Amsterdam-Frankfurt by Train
The best way to travel between Amsterdam and Frankfurt is by rail. Modern ICE trains run 7x daily from Amsterdam central station to Frankfurt airport and Frankfurt Hauptbahnhof (main station) - the journey takes just 3h 46mins.
The train makes stops in Utrecht, Arnhem, Düsseldorf and Köln (Cologne). The ICE runs at speeds of up to 300km/h on the Cologne-Frankfurt section.
The lowest one-way fare in 2nd class for the trip is €39, though availability is somewhat limited and fares of €49 to €69 are more common. Consider checking the 1st class price which can be had from €69 one-way.
Travelling by ICE train on this route is certainly far more comfortable and convenient than either air or bus travel.
For more info see International Rail Services to/from Amsterdam
2. Amsterdam-Frankfurt by Air
The 2 respective "national" carriers operate services between Amsterdam Schiphol (AMS) and Frankfurt Main International airport (FRA). Flight time is scheduled to be around 65 minutes.
KLM (Skyteam) flies a 6x daily Cityhopper service between Amsterdam and Frankfurt. Smaller jet aircraft are used on the route - Embraer 190s and Fokker 70s (which both have a 2-2 cabin configuration). Prices start at €99 return.
Lufthansa (Star Alliance) operates 7x daily on the AMS-FRA route using a variety of aircraft including Airbus A319/320 series and Boeing 737s.
Fares are similar to KLM with returns also starting at €99.
KLM and Lufthansa are the only viable options on this short flight route - you could also fly Air France (via Paris), British Airways (via London) or Czech Airlines (via Prague) - but these would be significantly more inconvenient as well as expensive.
3. Amsterdam-Frankfurt by Coach
Eurolines runs a 15x weekly coach service from its Amsterdam Amstel terminal to Frankfurt with stops at HauptBahnhof, Zentral Omnibus Bahnhof (ZOB) & Cosmopolitan Restaurant. Eurolines tickets in Frankfurt can be bought at Deutsche Touring, Mannheimer Str. 15.
The journey takes approximately 8 hours and return promo fares start from €22 if you book in advance and avoid the weekend.