You can claim airfare, taxi fare, rail fare or money spent on any mode of conveyance when you travel to another city to conduct business. If you have used your own vehicle then you can claim the money you may have spent on making the trip. Topic 510 gives you full details about expenses related to using your car for a business trip.
Business expenses and gifts are also deductible subject to limits. These are covered in full under Topic 512 and 463. It is mandatory that you keep a record of all the expenses you incur and put them up for deductions. Topic 305 gives you information on how to keep records.
It is also important to account for all expenses that you have made from an advance that the employer has sanctioned to meet the business requirements. Otherwise this income may become taxable income. To avoid this from happening, you must account for these expenses within an agreed time period; and return any excess amount within an acceptable time frame.
So work hard and be careful about your records. Both ways you could be getting cent wise, dollar wiser.