Trials began on the line between the Gogar depot and Edinburgh Park station in the west of the city for the first time yesterday.
Testing on this section of the track will eventually see more than 150 journeys per day, five days a week, and will continue until the full service is opened, which is planned for May next year.
Residents, commuters, pedestrians and employers and businesses in Edinburgh Park, Hermiston Gait and the Gyle Centre have been informed about the testing and reminded to be aware of the new vehicles operating in the area.
The section of track tested crosses the road in two places, at Lochside Avenue and South Gyle Broadway, where there are traffic lights, pedestrian crossings and the normal rules of the road apply, said the City of Edinburgh Council.
A safety and awareness campaign will be launched across the city before testing of the full route is carried out in December.
Councillor Lesley Hinds, the city's transport convener, said: "The project continues to move forward and ever closer to completion. We remain on track for a service launch in May 2014, although we will bring this forward if we can, and the importance of this testing, commissioning and driver training phase cannot be understated.
"Through carrying out all the appropriate checks and controls, we can ensure that the tram has been thoroughly tested before passenger services begin."
It was originally intended trams would run from Edinburgh Airport to Newhaven in the north for £545 million. However, they will now stop in York Place and cost £776m.
Last month, it emerged that a return fare from the centre of Edinburgh to the airport will cost £7.50 by tram while the faster bus journey costs £6. A single fare to the airport will be £4.50, compared to £3.50 on the bus. The cost of a single ticket on trams within the city centre will be £1.50, the same as buses charge.