How should I make the intention for Hajj? What should be recited after making the intention?

Make the intention for Hajj in your heart and also say aloud, لَبَّيْكَ حَجًّا or say, اَللَّهُمَّ لَبَّيْكَ حَجًّا. After finishing, continue reciting the Talbiyah. The Talbiyah is:

لَبَّيْكَ اللَّهُمَّ لَبَّيْكَু لَبَّيْكَ لاَ شَرِيكَ لَكَ لَبَّيْكَ إِنَّ الْحَمْدَ وَالنِّعْمَةَ لَكَ وَالْمُلْكَ لاَ شَرِيكَ لَكَ

Thereafter, proceed in groups toward Mina, whether by vehicle or on foot.