The wooden dummies we use for sword practice are to us what the boxing bag is for a boxer. They are a great tool for practising basic techniques such as cuts and thrusts, and improving precision.
The stick should be slightly thicker and heavier than a regular broomstick to give sufficient feedback when you hit it. Drill a hole in both ends so it can be suspended between the floor and the ceiling. The upper hole should be big enough for two cords so there is something to catch the wooden dummy if the main cord wears down and snaps (which will happen sooner or later).
The stick is tied up to the ceiling with a cord through the upper part. The lower part is secured to the floor or a heavy weight by another cord. Adjust the cords so that there is a suitable amount of flexibility to the dummy. When you hit it you want it to move easily without too much resistance, but you should still get a decent amount of feedback. Do not use a cord that is too thick – I use a 3 mm polyester cord which works well.
This design allows for quite hard blows and good feedback on the techniques, without harming either the sword or the dummy much.
Note that the dummy is designed for wooden swords or blunt metal swords. Sharp swords will cut into the wood and since the dummy will move on impact it might expose the edge to unwelcome strain.
Basic techniques like cuts and thrusts of every kind can be practised on the dummy. It is especially good for practising precision in thrusts.
It is also surprisingly good when practising simple footwork, such as stepping out of the line while doing a technique. Beginners can focus on where they put their feet without any distractions from a moving opponent.
By isolating the basic techniques and practising them on the wooden dummies, it is easy for the instructor to see and correct errors. You will also be able to perform many more repetitions compared to spending the same amount of time on application practice for example. Then when you do partner practice you can focus more on the dynamics of the application and less on the basic techniques.
If you don't have a training partner you can use the wooden dummy as a substitute when practising applications. It gives you something to focus your techniques on, and while it is not as good as a training partner it might be better than practising applications solo "in the air".
If you have two wooden dummies available close to each other you can try to use both when practicing applications - perform the defense on one and the counter on the second.
See this video for an example of wooden dummies in action: