The two most common methods are load cell and platform .
LOAD CELL
Believe it or not , most aircraft, even the largest passenger jets, can be jacked up on stands at 3 or more points. Load cells can be fitted in between the jacks and the aircraft in order to provide weight information. This method has the advantage that the aircraft can be set up and weighed in its normal flight attitude. This weights measured by each load cell can be summed to give the total weight and individually used to compute the centre of gravity. The complete weighing kit can fit inside a large suitcase making it highly portable. However there are important safety issues to be considered with this method.
PLATFORM
The platform system is now well established for aircraft weighing. Shallow ramps are placed in front of each undercarriage wheel with a weighing platform placed at the head of each ramp. The aircraft is usually towed or pushed up the ramps onto the platforms by tug or tractor. For large aircraft, the platforms required are large and special transport equipment is utilised.
The process of aircraft weighing with loadcells or platform scales is shown in de video's below
Weighing with loadcells
Weighing with platform scales