Am I legally required to pay taxes on the rent I collect from people living in these rooms I rent out in my primary residence?
If so how much are these taxes?
If this is merely a cost sharing arrangement where the amount paid is below fair market rental, there would be no reportable income to you. If the “rent” amount is fair market value, or more, there is still some question as to whether you even have to report it, as it almost always comes out zero. Most people take the attitude that it is not income; it's just room mates sharing expenses and ignore it. Family, as opposed to unrelated roommates, makes that position stronger.
Here’s what you may be required to do:
Report the income (enter at Rents & Royalties/Income & expenses from Rental Properties); and then deduct the expenses on schedule E. If the room mate has full run of the house, and there's just the 2 of you, then half your expenses are deductible (mortgage interest, property taxes, insurance, utilities, repairs, and depreciation [if needed}). Your net income will usually be less than zero*.
What you are NOT allowed to do, because it is your own home (you have "personal use") is claim a loss from this activity, to offset other income. Because of the "personal use rule", your deductions are limited to your income. Net effect ZERO.
It is possible for you to gain a positive tax effect from this activity; If enough of your schedule A deductions (mortgage interest & property tax) are shifted to Schedule E, and your standard deduction becomes bigger than your itemized deductions, you will have effectively saved on taxes.
If you have no mortgage, then there could well be profit involved, which you may have to offset with depreciation that could lead to "recapture" in the future when the property is sold.
For details see IRS Pub 527 https://www.irs.gov/publications/p527/ch04.html#en_US_2014_publink1000219159
*TurboTax (TT) does not handle this properly. TT will not limit your deductions to your income. You have to do that manually. TT wants you to enter this as a “not for profit rental”, which does not use Schedule E and puts your expenses on Schedule A (itemized deduction). I'm of the opinion that's not the proper way.