Before starting with the actual training you should always take some time to do a proper warm-up, even though many amateur athletes neglect this rather ‘boring’ part of the training. In fact, warming up is not only beneficial for Judo and martial arts but also for every other sport. A variety of studies have shown that performing warm-up exercises other than stretching causes an increase in body temperature and respiratory rate. Additionally, the heart rate rises which leads to more blood circulation and thus to an improved provision of oxygen and nutrients in the muscle fibers. All these processes, that happen in our body while warming up, improve the performance during the workout while reducing the risk of possible injuries at the same time.

Ideally, your warm-up should cover 5 to 15 minutes depending on the intensity of the following workout. As the purpose of warming up is to achieve improved performance during the training you should only choose low to medium intensity exercises in order to prevent fatigue and to preserve enough energy for later. Usually, the warm-up consists of two different phases. Firstly, you should perform cardio exercises or exercises that demand large muscle groups to increase the body temperature. Probably the most popular choice for this phase is simply running. I would suggest choosing a distance from 400m to 1 kilometer with a pace that feels easy for you. While running you use your calves, the quadriceps, the glutes, hamstrings, and also the core muscles for stabilization.
Another warm-up exercise, that demands the whole body, is jumping jacks. Thirdly, you could simply circle different body parts like shoulders, arms, legs, and hips for several minutes. Alternating these three options will help you to prevent getting bored while warming up.
The second phase of the warm-up focuses on preparing you for the specific sport you plan to do later. That’s why those are often exercise with similar movements or exercises that demand certain muscle groups which will particularly be stressed later. For Judo ukemi, the art of falling, is a great specific warm-up, since it prepares the body for great pressure during a throw. If you keep all these aspects in mind you are now ready to start your training!

Source: http://www.edu.xunta.gal/centros/iescastroalobrevilagarcia/system/files/WARM%20UP_0.pdf