A home office is only deductible if it's used for the convenience of the employer, meaning no work space was provided by the employer at the office. If your wife worked at home due to her own preference, none of the expenses would be deductible.
If your wife receives a W-2 for this job, you would deduct home office expenses as job related expenses on the Schedule A for itemized deductions. Deluxe handles itemized deductions.
The amount deductible is only the amount over 2% of Adjusted Gross Income, and only if all your itemized deductions in TOTAL exceed your standard deduction of $12,600 for a married joint return.
If she receives a 1099-MISC for this work, that would require a schedule C for self-employment and would require an upgrade to the Self-Employed version.