(2-part post):
Hi 237SJ.
Let's start with an important link:
http://www.bahn.de/i/view/GBR/en/index.shtml
The journey planner, there on the Die Bahn website, is wonderful because it incorporates the timetables of all European railways. You can ask it how to get from Cleethorpes to Moscow and you'll instantly get the whole journey planned for you!
That link lets you book certain services but, in general, you'll need to look elsewhere. You used to be able to buy tickets for European Rail travel from any principal National Rail station but that facility has been withdrawn. National Rail's official partner company is now Rail Europe:
http://www.raileurope.co.uk/
You can book online or by phone.
However many people prefer to use Die Bahn's UK telephone booking service. (See the panel on the right of the Die Bahn page I've linked to above). There are slight differences in the booking fees of the two companies, with either firm being cheaper for some journeys but dearer for others.
Many European rail operators also allow to book online (usually collecting your tickets at your departure station). Tell me which countries you're considering travelling to and I'll provide you with the relevant links.