The only time you report someone else's income on your tax return is if you are legally married and filing a joint return. If this is your unmarried partner, they file their own tax return for their own income, even if they qualify to be claimed by you as a dependent. (I will assume they do meet the qualifications, we can discuss this separately if needed.)
Assuming your partner qualifies as your dependent, they must have less than $4400 of total taxable income (wages, lottery prizes, self-employment from side gigs, and so on). In this case, they would not be required to file a return at all**, unless they had tax withholding and want it refunded.
(**If the person is under age 19, or a student under age 24, their parents are alive, and they have more than $1100 of unearned income--which is to say, income not from working but from investments, gambling, unemployment compensation, and so on--then they may be subject to the "kiddie" tax and may need to file a return.)
