"I can make all kinds of plans for travel but train travel seems confusing to me :("
Start by looking for schedules at the Bahn (German Rail) website http://reiseauskunft.bahn.de/bin/query.exe/en, following Rick's tutorial: http://www.ricksteves.com/travel-tips/transportation/trains/online-schedules
This site only has prices and booking capability for trains that start or end in Germany. For other routes, you usually want to go to the train website of the country where the train starts (there are exceptions of course). Here's a handy list, from The Man in Seat 61: http://tinyurl.com/bo8x6o6
If you aren't sure if advance purchase tickets will save you money, a quick way to find out is to price tickets for tomorrow and tickets for 2-3 months out. You can then see if there's a difference and how much it will be, and then decide accordingly.
Note that for some routes, there are different options with different price structures. For instance, from Amsterdam to Brussels, you can take local trains (prices don't go up, but it takes longer) or Thalys trains (faster, but prices skyrocket closer to travel, or if you can't work with non-refundable tickets). However, if you buy a Thalys on that route when it goes on sale (so you can snag the lowest price), it's actually cheaper than the local trains.
The Man In Seat 61 has all kinds of detailed train information; if you ever have questions about a specific route, he's a great place to start.