Breaking a vow to God is similar to breaking an oath. There is a hadith regarding this:
“ كَفَّارَةُ النَّذْرِ كَفَّارَةُ الْيَمِينِ ”
“The expiation of (the breach of) a vow is the same as the expiation of (the breach of) an oath.” (Muslim, Vows, 5)
Allah the Almighty commands about the expiation of oaths in the Quran as follows:
لاَ يُؤَاخِذُكُمُ اللّهُ بِاللَّغْوِ فِي أَيْمَانِكُمْ وَلَـكِن يُؤَاخِذُكُم بِمَا عَقَّدتُّمُ الأَيْمَانَ فَكَفَّارَتُهُ إِطْعَامُ عَشَرَةِ مَسَاكِينَ مِنْ أَوْسَطِ مَا تُطْعِمُونَ أَهْلِيكُمْ أَوْ كِسْوَتُهُمْ أَوْ تَحْرِيرُ رَقَبَةٍ فَمَن لَّمْ يَجِدْ فَصِيَامُ ثَلاَثَةِ أَيَّامٍ ذَلِكَ كَفَّارَةُ أَيْمَانِكُمْ إِذَا حَلَفْتُمْ وَاحْفَظُواْ أَيْمَانَكُمْ كَذَلِكَ يُبَيِّنُ اللّهُ لَكُمْ آيَاتِهِ لَعَلَّكُمْ تَشْكُرُونَ
“God does not take you to task for the oaths you utter unintentionally, but He will certainly take you to task for the oaths you have sworn in serious intention. The expiation (for breaking such oaths) is the feeding of ten desperate persons with the average of what you feed to your own families, or to clothe them, or to set one subjugated person free from bondage. Who does not find the means, shall fast for three days. This is the expiation for your oaths whenever you have broken them. But do keep your oaths. Allah makes clear to you His commandments, so that you may fulfill your duties.” (Al-Maidah/The Feast 5:89)
To feed ten person means to give them all meals like breakfast, lunch and dinner. You can also feed one needy person for ten days.
Feeding or clothing should be the average of your daily expenses according to your social and economic situation. You can also cover the expenses of their meals & clothes rather than feeding and clothing them.
The Almighty God commands in another verse:
“Do not use (the name of) God in an oath as an obstacle towards piety, mindfulness and reconciliation of people. God is all-listening, all-knowing. ” (Al-Baqarah / The Cattle 2:224)
Your oath must not be an obstacle to doing good deeds. If you took an oath of this kind, you must break it immediately and expiate for it.
 Reference : Sahih Muslim 1645
In-book reference : Book 26, Hadith 18USC-MSA web
(English) reference : Book 14, Hadith 4034 (deprecated numbering scheme)