To get the ladder you need to progress through the tasks given to you by Tom Nook. Pay off your tent payment and build your home. You will need to build Nook’s Cranny and the bridge. You will also need to build a bridge and furnish three homes for the villagers.
After all that, Tom will give you the ladder recipe so that you can head over to the island’s peak to get some flowers. The ladder will allow you to climb up or down different levels of the island.