The modes are found on the Thermomix screen by swiping right. Scroll down for more modes.
The two most used modes are the Scales and the Kneading function.
I suggest you occasionally check for updates as new and exciting things will be added regularly.
I rather love the egg boiler mode, it is such a relaxing way to boil your eggs and you don't have to hunt in the cupboard for an egg timer. Despite its instructions I find it works just fine with eggs which are not kept in the fridge, and with large size eggs.
Possibly the Thicken mode is the cleverest, particularly useful for those of you who like to use your own recipes. Read my explanation on my Thicken mode page here