A labyrinth (or house with different rooms) is a good project even a person with little DIY experience can realise.
Concerning size and distribution of the rooms there are almost no limits. The only thing I recommend is having every room with at least 2 doors (for ventilation and avoiding degus being trapped) and making some of the rooms big enough for being used as nest. You can even combine labyrinths of different sizes by piling them.

The labyrinths we have built so far are about 30x30 cm or 40x40 cm big. Smaller than 30x30 cm I wouldn't recommend as there is little scope for a good room arrangement.
Here are some of our examples:
30x32 cm

30x32 cm

40x42 cm


A good wood to use is a hard plywood (e.g. pine or beech), 10 mm thick. We also tried birch and poplar, but especially poplar is quite soft and no challenge for ambitious degu teeth. The height of the labyrinths is around 11 cm (10 cm the walls plus 1 cm the roof). The holes (here you need a hole saw) are 65-70 mm in diameter. Don't worry, your degus will make them bigger if they are not happy with them.

What you have to do:

Make a plan on how big it should be and how the rooms should be arranged as these measures are important for calculating the wood necessary for the walls and roof.
Here is an idea on how this could look like:


Total size of this model is 40x42 cm (being this the size of the roof), the walls being 10 mm thick for easier calculation. In blue are the "doors" in the walls and roof. But this is completely up to you and your fantasy.
I strongly recommend painting the roof with a suitable paint (one approved for children's toys) a couple of times and fixing some wood to the bottom of the roof to avoid it being moved.