What is the best way to make oats with milk when there is no microwave available?
I am not sure how I can warm it up without either burning the milk or making it taste bad.
A stove would be the traditional method for making oats and it doesn't require a microwave. It takes longer than the microwave but it works just fine, if not better (but this will vary by personal preference).
Add milk to a small pot, bring it to simmer, add oats to the pot, cook for recommended amount of time depending on the type of oats you're using (see package for times) or until they reach your preferred level of doneness. Some recipes have you add the oats and liquid at the same time and bring to a simmer together... either option works.
Make certain to keep the temperature low enough to not burn and stir occasionally to move them around. Milk is mostly water (about 87% in whole milk, higher in lower fat milks), so as long as you're not using extremely high heat and leaving it unattended for long periods of time, you should be fine.
Contrary to what most people believe, it is not necessary to cook oats.
There is a type of oatmeal called "overnight oats" in which the oats are stored with milk and other fruits and spices for at least 8 hours and up to 2-3 days in the fridge.
The oats will soften overnight and have a nice texture the next morning. The main difference would be the fact that the oatmeal is cold rather than hot. Check out this site for more details and some ideas.