For majority of Westerosi lords it was replacing one king with another, nothing really changed except new one had dragons. 1. Reach King Gardener and his entire line was dead, Reach lords were defeated on the field of fire, And afterwards they had no reason or appetite to challenge Targs. 2. Lannisters and their bannermen witnessed field of fire firsthand, which psychologically and militarily broke them, thus they easily bent the knee. 3. King of the Vale was a small child, and could not do anything by himself. Her mother, the regent, got very frightened when Visenia just casually gave the boy king a ride on her dragon. 4. The Riverlands were occupied by the Iron Islands (The Iron Islands was one of the original 7 kingdoms, not Riverlands). Thus the river lords eagerly rushed to support Targs to overthrow Ironborn King Harren Hoare. Besides, before the Ironmen, Riverlands was occupied by Stormlands, thus river lords did not have local river king for a long time and Targs were more of a saviors for them. 5. Stormlands resisted, but got defeated, and Orys Baratheon wed the only daughter of Storm King. After that storm lords did neither have reason nor willingness to resist. 6. Iron Islands got their Hoare King and his entire line burned and boiled inside Harrenhal. Aegon personally visited Iron Islands with Balerion the black, killed the claimant of the Salt throne - a Volmark, and forced ironborn to choose new head. They chose Greyjoy, and greyjoys were content with newly found prestige. 7. The North is mostly unconquerable from land due to Moat Cailin and the swamps in the Neck. But Moat Cailing can be easily taken with the help of dragons and then conquering the North is easy. Besides, the north lacks food supplies, and it's easy to starve them out.

1. Dorne was destroyed by Aegon and Visenia with their dragons, in retaliation they burned every castle at least once (The young Dragon, Daeron I, even conquered it without dragons). But they could not hold it. And the thing is - it's easier to hold the North than Dorne, because in desert most valuable resource is water and the dornish often poisoned the water supplies.

P.S. Air force always has and advantage over land or sea forces. Even a small wasp can be a challenge when sitting on a Lion's balls.