If you're coming from other cities or countries in Europe and want to get to Germany then visit the bahn.de site, at the top of the page you'll see a German flag wit (Deutschland) next to it. Click on the check mark to expose other languages. There's a US flag for English.
On the left hand side note the RAIL, HOTEL, RENTAL CAR, make sure RAIL is selected. For one way travel select "single journey".
Lets say you were taking the train from Munich to Dusseldorf. In the first box enter "munich" in the second box below that enter Dusseldorf, note if a box drops down you can select from the box, in this case "Dusseldorf City".
Cleck on the calendar to the right of the date to select your date of travel.
You can select trains by the your time of departure (Munich) or the time you want to arrive in Dusseldorf. Then click on SEARCH.
When the next page comes up you'll see what you entered at the top. Then trains are listed by date and time, also the duration of the trip. ICE means high speed train (Inter City Express) anything else is slower. Also note the "Chg" which means train changes. Often buying your train tickers in advance via the internet and printing your tickets can save you money.
If you plan on several trips or even an expensive one look into buying a Bahn card which sometimes allows for big discounts which save money and pay for the card.
Peak travel during rush hour is usually more expensive.