Pull up your inventory and equip the work uniform that Tom Nook provided you. If you want a new set of uniform, you can try heading outside his house, unequip the uniform, drop the uniform from your inventory, then go back inside and talk to him. Next up, he will give you some flowers and trees for planting. Go outside, find a nice spot, select the item you are planting, then plant it down. Sometime later, you can pick up the flowers once they have grown and you can use an axe which you will acquire later to cut down the tree.
After planting, go back inside the shop and talk to Tom. Now your task will be visiting the townsfolk. Use your map to search out the locations of the people you need to visit. First up, head outside of The Town Hall and meet the Mayor. Then meet all of the animals one by one. The animals are located inside their houses or outside the perimeter of their residential areas. If they are inside their house, knock on the door first and then talk to them. The animals will provide helpful information during the conversations. One of them will ask you about your birthday, take note of this as you will have lots of gifts and goodies from your neighbors during this date.
Now go back to Tom and he will give you a new job of delivering furniture. Just deliver the objects to the specified villager.
After the delivery work, you will be asked by Tom to write a note and send the mail to someone. Jot down the letter and send it out to The Post Office. You have to pull up your menu, choose the paper, and write the letter normally.
Your next work will be to deliver a piece of carpet. Simply look for the specific house and tell the villager there is a delivery waiting.
Next up on another delivery job is a watering can. Just deliver the goods as usual.
For the final task, you have to make an ad for Tom Nook's shop. Head to The Town Hall, look for the message board located there, choose New Message and write something for the ad, then head back to Tom once you are done.
Now you will be free from Tom's employment and you can play the game normally and explore all you want. If you have additional characters, they will have to do all the same tasks for Tom that you have done, however they will not receive any compensation like you did. It is highly advisable that you complete the tasks for Tom for all your other characters as several features of the gameplay will be unavailable if you don't. Immigrated characters however, will not need to do any of the tasks as they have already done them on their own.