When the Amavasya falls on a Monday, then it is called 'Somvati Amasvasya'.Somavati Amavasya , is no moon day that falls on a Monday in accepted Hindu schedule.This day holds utmost significance as you can perform several pujas and rituals.
On Somvati Amavasya, if you do the Tulsi parikrama 108 times, if possible. You can also, chant the 'Omkar mantra' and offer water and argh to the Sun God. All this will lead to happiness in your life.At home you can do small Havan on this day.Here is some information about Somvati Amavashya Puja vidhi at home.
Things to do Havan(Burning of Holy Hindu things Like Ghee,Aahuti and Coconuts)
Gauch Chandana or Kandan should be made into a vessel and make Havankund, then after collecting the above 8 items, all the members of the house gather and offer 1-1 of the deities given below.