One of the name of Lord shiva is soma - saha uma. For the Lord someshvara Who wears the soma, the moon crescent on the matted hair, on the somavara day (Monday), this festival is observed.
Though all Mondays can be observed as vrat there are special mondays when it is much more emphasised to observe like the shravan Somvar and karthikai SomavAr. According to skandha puran , on the Mondays of the month karthikai (mid Nov to mid Dec) this vrata is observed.
Way of observing
After taking bath pray to the Auspicious and Graceful Lord Shiva. Anointing the Lord with panchAmRitam and other pleasant substances, hail the Lord offering bilva leaves. During the day don't take any solid food. U can take Milk/ buttermilk/ fruit juice/ fruits . After 6'o clock in the evening pray to Lord Shiva and break ur fast and eat normal solid food (avoid onions and garlic) . Your fasting should start from 12 in the midnight and ends at in the evening on monday. It is believed that one who fasts on all Monday of Shravan has all prayers from the heart answered. It is not necessary to undergo rigid practices. Even for this fast, different people may have different practises....e.g. some people may not have buttermilk or some may have specific mantras to be chanted. You can follow whatever gives you a peace of mind.