This type of training is usually much quicker than hand training and is a helpful intermediate method. It works because degus are naturally inclined to enter long, dark spaces as they would enter burrow tunnels in the wild. It also allows them to feel more secure during transportation between play area and cage.
You will need a large cardboard tube, big enough to allow your degu to comfortably climb inside. The middles of carpet rolls are ideal and you can pick them up, usually for free, from carpet shops. The tube needs to be around 30 cm long or more (they can usually be sawn down to size).
Many degus will naturally be inclined to enter the tube when it is offered up to them, however if your degu is a little more shy, it may help to keep the tube in your hay or feed bag so that it smells inviting to them. You can leave the tube inside their cage on the floor for half an hour or so every day, with a treat inside (try porridge oats). This will encourage your degus to investigate the tube and associate a positive reward with going inside.
Once your degus are happy to go in and out of the tube, you can try tapping the tube gently when you put it in the cage before they go in and get the treat. This sound helps them to associate the action of entering the tube and the reward, so that later you will be able to tap the tube to ask them to get in and they will understand.
Once your degus have got the hang of getting into the tube, tapping and rewarding, it's time to try gently picking up the tube while your degus are inside. At first you need to do this very slowly and only lift the tube a little, to avoid scaring them. At this point you must be very careful not to trap your degus inside the tube- they need to feel that they can get in and out if they choose. It's all about building up their trust in what you are doing.
Slowly build up your movement as your degus get used to it and reward them after doing so as soon as possible. Your aim is to be able to move the tube and degus in and out of the cage without them panicking. Don't be afraid to spend a long time getting this right, or to go back a stage if need be.
When you think your degus are ready, use the tube to move the degus from the cage to their play area, then give them a treat as soon as they come out of the tube. At this point you can leave your degus to play as normal, but keep the tube elsewhere. Once it's time for them to go back home, offer the tube up to your degus and tap it, and they should hop in to get their treat. You can then move them back home and reward them again. Remember that the first time you do this might take a little while, but be patient and they will get there in the end! Never try to force them into the tube or you could end up undoing all your hard work!
When moving your degus between the cage and play area it is a good idea to gently place a hand over each end of the tube, just to stop the degus jumping out and injuring themselves. If you move slowly, calmly and talk to them softly by doing so your degus should remain relaxed on their short trip.
Repeat this training as often as possible and after a month or so you won't need to keep using treats all the time, simply offering the tube and tapping it should be enough as your degu will have got the hang of the process and know what to expect. Most degus are motivated enough by the prospect of getting out to play!
As an alternative to using a tube, you can also use a small travel/carry cage with oats sprinkled in the base. Many degus are very happy to climb into one of these offered up to the cage door to eat the oats. You should build up the training in the same way as with the tube.

Thanks to Melissa for this tutorial!