Apart from in the Judgement game mode, a player will need to construct decks from their library of scrolls which they'll then use to play in the Trials, against the AI, and also in the Ranked game versus other players.
At the start of the game each player will be given a set selection of scrolls that are formed into pre-constructed decks that can be viewed via the deckbuilder. The decks are specifically constructed to give players an understanding of that resource types primary mechanics and also the general mechanics of Scrolls. If you have played through the tutorials then you should be familiar with Scrolls' mechanics (such as unit placement and movement) and also with some aspects of the the general mechanics of a Collectible Card Game (CCG). If you wish to know more then you can read about these mechanics, and the more complex ones, in other Academy articles.
You gain new scrolls by playing the various game types to earn gold and by either purchasing individual scrolls (or scroll packs) in the store, or by trading with other players in the trade channels. For new players, it can be quite daunting to see the number of possible scrolls to purchase so I would suggest talking to other players in the chat channels or check out the deckbuilds that are available at Scrollsguide and Scrolldier. From this you will discover what the best scrolls are for your resource type and, perhaps, what type of deck you want to build.
Players will learn the game more effectively if they adapt their deck over time with each new scroll they buy, learning how the scrolls interact with each other, rather than jumping straight to a 'meta deck (a deck that appears to have the least number of weaknesses). They may have a deck that is more likely to win at the earlier stages of ranked play, but more skillful players will have an edge on them anyway due to playing experience and deck experimentation, even if they have an inferior deck.
CCGs are all about the quest to learn what the most powerful decks are and being able to construct those deck with the scrolls you have available in your library. If you have enough skill, you may even find a new meta deck which counters the current most popular one. Ultimately, though, it's the joy of discovery that makes the Constructed game mode so enjoyable.
Combat, unit values, units attacking, and units being attacked is explained in this guide aimed at new players.