The taxable portion of your grants should be reflected on your form 1098-T from the school. When there is taxable grants, the amount in box 5 for form 1098-T is greater than the amount listed for billed or paid tuition and fees in boxes 1 or 2. If you enter the 1098-T into the education expenses section, TurboTax will properly record the taxable portion as income.
See this explanation from IRS Publication 970:
Pell Grants and Other Title IV Need-Based Education Grants
These need-based grants are treated as scholarships for purposes of determining their tax treatment. They are tax free to the extent used for qualified education expenses during the period for which a grant is awarded.
Follow this path in TurboTax:
Go to the Federal Taxes category (or Personal Income for Self-employed).
Go to the Deductions and Credits subcategory.
Click on the “I’ll choose what I work on option”.
Find the section labeled “Education”.
Click start or update on the line labeled “Expenses and Scholarships (1098-T)”
Enter your 1098-T. The income will show up on Form 1040 on line 7.