Firstly you must make yourself familiar with the  International Standards on Unicorn Husbandry (ISUH for short) or you risk your Unicorn being ceased by National Animal Care.

Comfortability 

Before you acquire your Unicorn you need to identify the right space.  The minimum requirement  for housing a UK standard pet Unicorn is 2m by 2m perimeter with 4m in height so that they are safe.  Next, they require nesting materials such as hay and a blanket to keep them warm and comfortable. 

Now you have received your Unicorn phone the Administry of Animal Care to ensure it is registered and to make sure you have met all the requirements for housing a Unicorn. This means they know where all the Unicorns are.

Trust 

Once you have acquired your Unicon it is essential to build trust, if they do not trust you they will not eat the food you provide so for the first month you have to feed it anonymously. 

Diet 

Fruit, vegetables and occasional meat are the basics of a Unicorn diet.  Artificial sugars are extremely dangerous to Unicorns, kind of like dogs and chocolate, therefore you must make sure that they do not have any.  Also, they are particularly fond of nuts which you can use to train them or modify their behaviour. 

Exercise

It would be great if you have a field to exercise your unicorn in so that they can run around safely.  They enjoy games like hide and seek since they have an adventurous spirit.

Finally, having a Unicorn may result in you having a friend for life so make sure you spend time with it everyday and enjoy it.