If you're an employee who is reimbursed for expenses you'll need to file and expense report for your employer, which is a written accounting of your expense while on travel. If you received a cash advance, you'll also need to return to the employer any amounts in excess of your expenses.
Some per diem arrangements and mileage allowances called "accountable plans" take the place of detailed accounting to the employer, if time, place and business purpose are established.
Where expenses aren't fully reimbursed by your employer or excess reimbursements aren't returned, detailed substantiation to IRS is required and, if you're an employee, your deductions are subject to the 2 percent floor on miscellaneous itemized deductions.
In addition, your expense records should be "contemporaneous," that is, recorded close to the time expenses are incurred.