im traveling to Netherlands/Belgium in May 2019. From Rochester NY USA (YYZ the closest international airport) to Belgium. Probably 7-9 days total. Flying out of Amsterdam back to the US......

any tips will help to keeping cost down ! TY

The airlines use complex algorithms to set airfares making it extremely difficult, if not impossible, to predict when they might go up, down or just remain static.

The best advice anyone cane give you is to monitor fares to your intended destination so you get an idea of the general price range. Then when you see a fare you can live with go ahead and book your ticket. The fare you find one day may not be there the next day.

HINT: You can sign up for airfare alerts on your airline(s) of choice and travel websites.

I would just enter your airports and dates online and start poking around at various websites. I start with Kayak, Expedia, etc. and then go to the airline's own websites once I have an idea who flies the routes.
Keeping costs down often involves making multiple stops or too long or too short or just generally inconvenient layovers. So sometimes it's a matter of how much more you are willing to pay for a more favorable trip plan. ~suze

There are a huge number of website that will help you to get cheap air flights as well as cheap hotels. Some amazing website that will help you are google flights, airflightsreservation, kayak, airlines flights, tripadviser, etc are the best websites.

Hope this will help you to save some money!