Here's the proper way to do it.
I live in a two-family house, living in one unit and renting out the other. The square footage of both units is approximately equal.
I file Schedule E for the rental unit. It shows 100 percent of the rent received as rent income. Most expenses are pro-rated, so Schedule E shows 50 percent of the property tax and 50 percent of the mortgage interest as expenses. (I actually show the full amount and the 50 percent calculation on the form.) Other expenses that are pro-rated include insurance, utilities, repairs to the grounds and common areas, etc. If there are repairs that are specific to the rental unit - let's say their sink needs a plumber - I show the full amount of the repair, 100 percent.
The other half of the mortgage interest and property tax - i.e. the half corresponding to the unit I am living in - are deducted as personal expenses on Schedule A. You can't deduct the other half of most other expenses (insurance, utilities, repairs, etc).
If the space rented out is more than 50 percent or less than 50 percent, use the appropriate percentage for the rental unit and the rest for your personal unit. You can calculate it based on square footage or number of rooms.
You can also take depreciation expense on the rental portion of the property; typically you can depreciate the building but not the land. You show the depreciation on Form 4562 and then transfer the amount shown to Schedule E. How to calculate depreciation is very complicated and depends on when the rental property went into service. You can look at the IRS publications on depreciation but you're probably going to need to consult with a tax professional.
You do not need to file Form 8582 (renting a home is not a "passive activity"), you are not a real estate professional, and you can still declare a profit or loss on your Schedule E in addition to your principal source of income.