In the name of Allah the most gracious,most merciful.
Assalam o alaikum,
Respected Sir,
My question is , if I had made promise to Allah and then some how it is broken then, what should I do and how ?

Go to the head cleric at your mosque and tell him what promise was broken and how. He will tell you what penitence you must do for forgiveness.

Hello

I hope I have gotten this right as I don't know too much about Allah nor Islamic religion .

I would go see from what I know and I hope I am correct the Grand Mufti or the highest religious leader at your mosque.

After talking with this leader / high member of the mosque , he will be able to tell you what you need to do to be put back on the right path .

It could be praying , community work plus other things .

Hope this helps.

My question is what Islam says if my promise made to Allah is broken? What should I do if same thing happens to me, that I promise to Allah that I will not do this thing again and some how I couldn't keep my words/promise?

What is this promise that you cannot keep?