There are several ways to obtain new dragons for your Berk and fill out your Book of Dragons! These activities include but are not limited to:

• Toothless Explorations: Hiccup and Toothless can search for dragon eggs on the islands around Berk. You can choose from a list of dragons (based on Toothless' level) to search for. Note that some of these are limited time, and will rotate out once their time is up. To send them out to explore, tap the "Search" button above Toothless' roost (left of your Meade Hall), then choose the Dragon you want to find. You can learn more about Explorations here.
• Journey: You can send Riders and their dragons out on journeys to adventure and find loot. This includes dragon eggs. To send a Rider out on a journey, select a Rider dragon (Toothless, Meatlug, Stormfly, Hookfang, Barf & Belch) and tap on the "Journey" button on the bottom of the screen. You can learn more about Journeys here.
• Card Packs: Card Packs can contain all kinds of loot, from resources to dragons! While Card Packs are available to obtain through various activities, the main way is through the Berk Market. You can access it by tapping the "Market" button on the menu at the bottom of your screen and selecting the Card Pack icon.
• Season Pass: The Season Pass contains several goodies for you to claim, including dragons and Card Packs that may offer a chance at obtaining a dragon. The Seasonal Market also allows you to use your Seasonal Currency to obtain even more dragons. To access the Season Pass, tap the "Season Hub" button at the top left of your screen. You can learn more about it here.
• Collections: Collections allow you to trade in your Collectibles found in Explorations, Journeys, and Card Packs in exchange for dragons and other rewards. To access Collections, tap the "Berk's Duties" button on the bottom menu and select "Collections". You can learn more about it here.
• Ascension Portals: You can use your Scales obtained from ascending your dragons on Ascension Portals. Ascension Portals offer you the chance at a limited pool of random rewards, including dragons and Card Packs that include them. To access Ascension, tap the "Berk's Duties" button on the bottom menu and select "Ascension". You can learn more about it here.

There are no shortage of ways to expand your family of dragons, so get out there and explore!