How to Earn Leaf Tickets:
Although sold by packages via IAPs, Leaf tickets are actually rewarded generously in the game simply by performing or fulfilling different tasks in the game, and every time you level up as well. We've listed below some of the usual ways to earn Leaf Tickets, as well the stuff that you might want to consider spending them on.
What are Leaf Tickets for?
If Bells in the game are the basic currency in the game, then Leaf Tickets are basically the Premium Currency. When compared to other free-to-play mobile app games, Bells would generally be the Coins, accompanied by a "Premium" currency like Gems -- which in this game are called Leaf Tickets. Leaf Tickets are mainly used to buy special items in the game or to expound on something that is usually limited like Crafting slots, market boxes, instant access to Shovelstrike Quarry, throwing net to catch multiple Fish at a time, etc. Basically, they tend to give you a shortcut on things that will usually take a longer time to do or that are tedious to do. Much more, they can also be used to speed up the construction time when you are crafting a Furniture/amenity in the game.
How to earn them:
When you level up - every time you level up in the game, you usually earn a thousand Bells along with 10 Leaf Tickets. Since it is relatively easy to reach level 25 in the game, you'll have plenty of Leaf Tickets to buy you stuff like Tom Nook's Chair and K.K. Slider's chair.
Complete Leaf Ticket rewarding goals - the game enlists different several goals that you can attend to while playing. Basically, the harder the goal is, the better the reward gets. Although not all of the listed goals in the game reward you with leaf tickets, there still are plenty out there to get you by without the need for any real money purchase.
Link your nintendo/social network account - if you don't have a Nintendo account, you can easily create one in their site. Simply by linking your Nintendo account, you'll be gratified with a hundred Leaf Tickets. Not limited to this, you may also link your social network accounts for another Leaf Ticket bonus. This is pretty much a one time deal but nonetheless give you a good amount of Leaf Tickets for free!
Via micro-transactions (IAPs) - to get you ahead of the game and you want to skip all those wait times in the game (construction time on Amenities/Furniture or having to wait for friends' help in the Shovelstrike Quarry), you may simply purchase Leaf Tickets with real money via micro-transactions. Leaf Tickets are sold in packages which are sold in relatively reasonable price (for a good quality game). As with any free-to-play game, the bigger the item bundle you purchase in the game, the higher the discount.
Where to use Leaf Tickets:
Purchasing Limited Time Items - there are special characters in the game which you can invite to your camp by buying special items that can only be purchased using Leaf Tickets. Some of the latter Amenities or Furniture to purchase may also require Leaf Tickets to Craft. Needless to say, trying to earn these new stuff would generally mean unlocking new content in the game -- which is basically what you are trying to do in the game.
Purchasing later-on Furniture and Amenities - later on in the game (as you get to unlock most furniture and amenities in the game), you'll eventually need Leaf Tickets to Craft furniture and amenities as they start to get harder and more costly to build.
Skip waiting times in Crafting, Shovelstrike Quarry, and Fishing - constructing anything will always take time in the game. Usually, the bigger the item or the harder it is to Craft (meaning having more hard to earn requirements), the longer it takes for Cyrus to build it. To skip the wait time, you may use Leaf Tickets. Be wary though as it can cost you a lot, especially when trying to skip out on very long wait times.
Not limited to this, you can also use Leaf Tickets instead of having to ask for your friends help to enter the Shovelstrike Quarry. Take note that this is quite expensive to do (20 Leaf Tickets) compared to having to ask only 5 friends to help you out. Just make sure to ask friends/people whom you always know are playing the game the same time you are.
Also, you can catch multiple fishes at a time using a net. When Fishing, you have the option to pay leaf tickets to "Throw Net", and catch multiple fishes at a time. Although you might miss out on the very joy of the game's fishing activity, it is helpful to know that you have this option.
Purchase additional slot in Crafting - initially, you can request Cyrus to Craft you Furniture, one at a time. As you progress in the game and earn sufficient Leaf Tickets, you can easily expand this capacity and make it up to 3 items crafted at a time. By doing so, you technically get to unlock things much faster in the game.
Purchase additional slot in the market - the same goes when trying to sell stuff in the market. In order to list more items to sell at a time, you can permanently expand your market slots by purchasing them with Leaf Tickets.