Can I include the rent I pay for my apartment as a tax reduction on my 1099. If so, what section do I add it under?
No. Rent you pay for your primary residence or 2nd home is not tax deductible on your federal return. However, some states do have a "renter's credit" on the state tax return. But you won't deal with that until you get to the state return, and only if your state offers such a credit.