Income reported in Box 7 of a 1099-MISC, "Non-employee compensation", is considered self-employment income by the IRS, and is reported on Schedule C of your tax return. You may deduct your allowable business expenses on Schedule C. You may only deduct actual expenses paid.
The IRS considers you a self-employed "business" in this situation. You can use your own name & address as the "business" name and address on Schedule C, unless you do your self-employment work under another name (such as "Jack's Handyman Services.")