How can you relief pain in these areas after martial arts training?

What areas?: I'll try to answer your question, based on my own injuries in martial arts training. For general aches/bruises after training, the best thing is a cold compress. Apply for 20 min over the bruise to not only reduce pain, but reduce swelling/bleeding in the injured tissue. Avoid aspirin/aspirin containing products. Massage can help relieve pain, along with topical pain relievers.

Stretching: It is important to stretch prior to workouts, but moreso after your workout session. Take advantage of the muscles being warm to slowly elongate and relax them after the workout.