Decide when you want to depart. Trains leave Amsterdam Central Station for Osnabruck roughly every two hours.
Think about how fast you want to travel. Most trains from Amsterdam to Osnabruck require at least two connections, but there are a limited number of direct trains. There is a slight premium for direct trains, which take around 2 hours less to reach Osnabruck.
Consider booking a ticket in first class, especially if you're going to make multiple connections. The lengthy travel time can be compensated by roomy seats and more leg room.
Try to get your fare reduced. When you book the direct train from Amsterdam to Osnabruck, you won't have much luck in getting a cheaper fare. However, if you look at booking each leg independently, you may be able to take advantage of discounts offered by both Netherlands Railways and Deutsch Bahn.
Figure out a payment plan. How you pay will be partially influenced by your itinerary. Travelers with little time to spare may prefer the convenience of a credit card payment. Otherwise, you'll have to stand in line at the international desk at Amsterdam Central Station with cash in your pockets.
Pick up your tickets at the Amsterdam Central Station well before you plan to travel. By giving your ticket confirmation number, you can collect your tickets from a customer service agent. Arriving early will ensure you have plenty of time to make your train.