Typically, it's simple.
Many companies have a Visa or MasterCard linked to a corporate bank account. All you need to do is provide your travel information (name, address, passport information, etc.) and pay for your trip with your corporate card.
It should be noted, however, that sometimes at check-in at the airport, the airline may ask you to physically present your card.
As an alternative, you may present a certified letter with a copy of your card stating that payment was made with the card.