Last min flight? How long can I wait?

Booking in Europe is a lot like booking in the US. Last minute bookings are always expensive and planes can fill up since their capacity is much smaller than trains. So you should consider booking as earlier as it is convenient.

Or you can always do your travel by train....

Train to London is one thing, train it Geneva is 10 hours+.
Why not look at some dummy bookings for cheap and traditional airlines for that time frame and then for a week from now.

I am familiar with buying tickets for flights within Europe, not so familiar with booking flights within other continents.
Buying tickets online is easy, just go to the airline's website.
Finding which airlines fly which routes is also easy. Go to Wikipedia, find the page for your departure airport. All these articles have a section "Airlines and Destinations" (example: https://en.wikipedia.org/wiki/Amsterdam_Airport_Schiphol#Airlines_and_destinations ), which list all airlines and their destinations from that airport.

• Buy your tickets early if you want cheap tickets, at least 2-3 months in advance, especially for the economy airlines. I.e. for August, buy now.
• Prices only ever go up (applies to flights, 90% of the time, and for trains 100% of the time).
• Do not forget many airlines charge extra for hold bags. You need to pay for this when you buy your ticket, Paying for bags at check-in costs a lot more.
• Check in online.
• Do not book onward travel (neither rail nor air) for the same day you arrive. You cannot predict when you will get out of airport immigration. Rail travel to elsewhere in Netherlands or Belgium is OK, as you do not need to buy those tickets in advance.
• Buy rail tickets from the website of the company running the trains.
• Flights only get you to airports. To get into cities, and even more so to get to towns without airports, requires additional transport, mostly by train. This skews the calculation for end-to-end travel times in favour of using trains all the way.
• If you want to spend time in Switzerland, Geneva and Zürich are not where you want to go, Go into the mountains instead.

A search engine like www.skyscanner.com can do a wide search (e.g., from Amsterdam to "Switzerland" so that more airports are considered), based on prices sold by the airlines themselves (usually connecting you directly through to complete a booking).