Yes, for many airlines you can start a date change yourself from the booking screen without ringing anyone, although how far you get depends on the airline and on the fare rules of the ticket you sold.
Where the airline supports it through the API, the process is simple. You open the booking, choose the new date, and the system comes back with the new flight options and tells you what the change will cost, which is usually the difference in fare plus whatever the airline charges for changing. Once you accept, the ticket is reissued and the updated details go to your customer. You can add your own service charge on top if you want to.
It will not work this way every time, and it is better you know that now. Some fares are simply not changeable, and the system will tell you so rather than let you try. Certain airlines, including a number of the low cost ones, do not offer a change function through their connection at all, so the request has to be handled manually with the airline or through our support desk. Part flown tickets, group bookings and tickets bought on your own negotiated deals also tend to need manual handling.
Before you promise a customer anything, open the fare rules shown in the search results, since that is where the change conditions sit, and ask us which of the airlines you plan to sell support online changes on the plan you are taking.