Begin by moving in some way to raise your heartbeat and get your blood moving. Some people like to do some running, other people hate running with a passion. It doesn’t really matter what you do as long as you are doing something simple with the purpose of getting the blood moving – a good sign is that you need to breathe faster as a result of what you are doing. (Personally, I prefer doing some gentle but large cuts with sword in hand, to get my blood moving without having to go for a run.)
Then take your various joints through their range of motion. For example, circle your arms so that you make your shoulders move in all directions, or turn at the waist. If you cannot move very far in one direction at first, this is not a problem, just do several gentle repetitions until you begin to feel yourself loosening off. Don’t push anything sharply or you will risk injuring yourself.
The ideal warm up is full of motion. Big motions can function perfectly well as a gentle dynamic stretch while also keeping the blood moving, and are generally better than deep “static” stretches while you are warming up for a session.
Holding these deep static stretches is not very good for a warm up (although you may often see people doing this). In general, movement is better for warming up, whereas deep static stretches are better during a cool down at the end of a session or for general flexibility training at other times outwith the session.
You absolutely can warm up with sword in hand. Make your motions large, almost exaggeratedly so, and don’t worry about “realism” – this isn’t a fight, this is just warming up. Begin slowly and at a low intensity, and gradually build the speed so that people are breathing faster. Any exercise you choose should involve the whole body, not just a single limb or joint.
If you want to warm up with sword in hand, then you could use for inspiration any of the exercise videos that follow. Yes, they are all technical exercises that you can use to improve your fencing skills. However, they can also all function as perfectly good warming up exercises, and I use all of them at my own club for precisely this purpose. This means that the first five to ten minutes of any session serve both as warm up and for revisiting fundamentals of good technique, which makes your training time more efficient, especially if you only have limited training opportunities during the week.