How did the small states get what they wanted in regard to representation in the new constitution?
A compromise. The small states got what they wanted in the Senate and the large states got what they wanted in the House of Representatives.
The small states initially wanted a legislative branch based solely on the number of states, like the legislature in the Articles of Confederation that didn't work
The large state initially wanted a legislative branch based solely on the number of people or population.
The Iroquois model of a confederation made up of five tribes, two large and three small was used to solve the conflict between the small and large states. The Iroquois had a legislature made of two bodies. One the council of chiefs had two chiefs from each tribe giving equal power to the small and large tribes. The Other council had one Representative from each long house. This gave the larger tribes more power based on their larger population. ( Note the representative from the long house was elected by the women of the long house)
The Connecticut Compromise proposed by a small state was based on the Iroquois model. This allowed the small states to have equal power in the Senate, while keeping the large states happy with their greater power in the House of Representatives.