How do I make money by renting out my house, on which I pay a mortgage?

Depends upon whether you chose wisely or not.

When looking at cash flow be sure to factor in the tax offsets from the mortgage interest you are paying, and the depreciation you get to take now that it’s a rental. And, any expenses maintaining it are now deductible from your taxes.

Could be that all the tax deductions make it break even instantly.

It depends on the type of loan you have. If you have an FHA or VA loan, at least one year before the loan is taken, the borrower must live in that home because the mortgage lender will check from time to time to see if the owner is still living on the property. But in general, before renting your property, it is in your best interest to read your mortgage agreement to make sure that there is no prohibition against renting a home, as it is possible that your mortgage lender will not rent your property. It is better to consult with your mortgage lender and clearly explain your purpose. For example, are you planning to rent the whole property or just one room? These details can make a difference for your mortgage lender.