There is a European Rail Travel forum, so I suspect you'll end up over there...

The answer is... It depends. There are international rail booking sites, but they charge a hefty premium - and railpasses can be subject to all sorts of supplements that aren't clear when you purchase. Up to you if it's worth it for the convenience.

But you need to remember: Europe is not a country - there is no European train system. It's a lot of countries, each with their own rail networks and characteristics, and in some cases multiple rail networks and dedicated international carriers. Sometimes it's priced like airline seats on longer journeys - buy early with inflexible tickets and it's cheap, but buy on the day and it's prohibitively expensive. With others, you just walk up to the counter and buy (or even buy on board). In some places you need an early reservation to guarantee a seat - in others, you're pretty much guaranteed one whenever.

The easiest is probably if you suggest where you're considering travelling - then we can give you a better idea of what's in store!

The actual travelling is the easy bit. With very few exceptions (mostly the Eurostar and Spanish AVE services) you just turn up at the station and walk on to the train, storing your luggage yourself.