Bells are the main currency of Animal Crossing: Pocket Camp. They have a wide variety of uses, from crafting/purchasing furniture, to upgrading the size of your camper. Bells are also much scarcer than in the console games, due to the drastically reduced selling price of bugs and fish. As such, it is important to take every opportunity to earn bells that you can.
The main way of earning bells in the game. Fulfilling an animal's request rewards you with a decent sum of bells, depending on the rarity and quantity of the resources given. Every three hours, a random animal will show up at each of the four vacant spots on the map (Lost Lure Creek, Breezy Hollow, Saltwater Shores, and Sunburst Island). In UTC, these resets occur at 12:00 AM, 3:00 AM, 6:00 AM, and so on. You can complete up to three requests for each animal for a total of twelve requests every rotation. Using a Request Ticket on an animal will cause them to make three more requests. You may also use a Calling Card to call another animal to your current location, adding another three requests.
In addition, every three hours, three random animals visiting your campsite will have a request. It should be noted that the cooldown for this works differently from the rotating animals. Instead of being at fixed intervals, the timer starts after you fulfill one of their requests. As such, it may be worth it to prioritize doing these requests to get the timer starting ASAP.
Talking to the animals visiting your campsite may result in a small gift of bells. The maximum amount varies depending on your friendship level with the gifting animal, but in most cases, it will be 100 bells. This can be done once per hour. Similar to their requests, this cooldown starts one hour after your first conversation, and affects all villagers (i.e. the last villager you talk to will reset one hour after the first villager you talked to.)
Bells are one of the base rewards from the Shovelstrike Quarry minigame. They can be earned regardless of what the bonus reward is. Bells may also be the bonus reward, resulting in much higher bell payouts, but forfeiting all resource drops. Players that do not wish to spend Leaf Tickets to play the minigame are limited to one attempt per day, so they should consider whether the extra bells are worth sacrificing the resource rewards. Resources and essences may seem plentiful early on, but they do run dry as you progress, particularly when upgrading amenities.
In addition to playing the minigame, simply helping a friend enter will award you with 100 bells, paid after they enter the quarry and play the minigame. If they fail to do the minigame before the daily reset (at 6:00 AM UTC), you'll get 10 bells instead.
Once per day, shaking a tree will result in a bag of 300 - 1,000 bells dropping. Any non-fruit tree is a candidate for this, including trees that insects can be found on at Sunburst Island. While it may seem like a pitiful amount, it takes virtually no effort and only needs to be done once per day.
Resources (such as bugs or fish) may be sold for a small sum of bells, either to the Nooklings, or to other players via the Market Box. Selling the item to the Nooklings will always result in the lowest price (half of the minimum Market Box listing price), but gives guaranteed bells instantaneously. Listing an item on your Market Box gives you a better deal, but selling items takes time. In addition, the item cannot be reclaimed and its price cannot be changed after putting it up for sale, so if you set the price too high, there's a chance your item will never sell.
Whenever the app needs to download a lot of new data, a minigame can be played as the download occurs. It's an endless runner type of game, similar to Super Mario Run, where you control a camper and have to collect as many coins as possible as you drive to the right. Each coin awards you with 10 bells, the total being sent to your mailbox when you enter the game.
Bells are a possible login bonus. If you really have no time to do anything else, you should at least try to log in everyday just to claim the login reward. Even discounting the bells, the login bonuses have some pretty useful items, such as resources and Leaf Tickets.