Tudor - don't worry, this is quite normal.
You need to make sure of a few things though:
1) You printed it on A4 paper (size 29.7 cm by 21 cm, or 12 inches by 8.4 inches) rather than something tiny
2) Don't tear the dotted line yourself (or at least, don't tear it completely) - leave it to the agent at the gate to do so
3) Keep the half you are given back at the gate - you'll need to show it when you climb the steps and enter the cabin
4) Don't lose it until you're off the plane, have collected your luggage and have exited the destination airport. If some official at an airport wants to be awkward, showing paperwork can help make them go away !