Does an aircraft use its engines to taxi or is it always pulled by some other vehicle?
I have seen a small lorry pulling it sometimes; is it really pulling the huge thing, or does the aircraft use its own power somehow?
Aircraft are not always moved with tugs (the small vehicle you refer to). Much of the time, they operate under their own power.
Airliners are generally pushed back from the gate using a tug, as that's the simplest and most efficient method. They then taxi to the runway (and all the way up to the gate, after landing) using their own engines to provide thrust. This is true of both jets and propeller aircraft.
Some work is being done on self-contained electric-powered ground propulsion; one major player in this area is a company called WheelTug. They use high-torque motors and the aircraft APU to allow the aircraft to move itself without starting its engines or requiring a tug to be connected and disconnected.
Usually an aircraft taxies under its own power. Aircraft have no powered wheels, so the forward thrust comes from the engines. Only pushback from the gate is mostly done by a tractor, although some aircraft can use reverse thrust for that.
When the aircraft is being moved for maintenance purposes or simply relocation at the airfield, the aircraft is usually pulled.
Research is going on into fitting electro motors into aircraft wheels so that they can taxi without having to start the engines. Lufthansa has done some experiments. The concept would save taxi fuel and is more friendly to the airport environment (noise, polution), however the additional weight of the motor drive system would offset these benefits because it causes additional fuel burn during flight.
Most aircraft taxi using their own engine power. Tugs are usually only used to get an aircraft to a safe distance away from all structures, people, and other aircraft before engine start, or if the engine(s) are inoperable (maintenance, mothballing, etc.). However, there is a system (called the ElectricGreen Taxiing System, introduced at the 2013 Paris Air Show) that attaches to the wheel and uses an electric motor to move instead of the main engine(s). It is currently only available on the Airbus A320 family and the Boeing 737 family.