?Do you purchase a rental property the same way you purchase a home for yourself?

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Do you purchase a rental property the same way you purchase a home for yourself? For example:

Rental property is $50,000
I have the down payment but will need to borrow money from a lender to pay the property.
Say all goes well, would I used the income from my tenants to pay off my rental property's mortgage? Or is there other ways of going about paying it off? (OR do I have to get a mortgage for a rental property at all?)