If you currently have a starter deck and want something a little bigger, you can either purchase one from a shopkeeper or find one as a drop from a creature or quest.
If you already have a second deck, you need to equip it, and then place your cards in it as you would like. To equip your new deck, press P on your keyboard when you're not in a duel and select the deck you would like to use. You can either double click it to equip it, or use the hand icon at the bottom of that screen.
Your wand automatically places a number of minor spells in your deck, and amulets and pets will often times put a spell card in your deck. If you have more than one deck, you can scroll through them by clicking the arrows around the deck title or pressing CTRL-K on your keyboard when you're not in a duel.
Now to build your new deck. Press P on your keyboard when you're not in a duel. This will open your deck.
To put a card inside your deck, simply click on it on the right side of the screen and it will show up in your deck contents on the left. The red circles next to the card shows the max number of copies you can put inside the current deck. The yellow circles show the number of that card that you have already put into your deck.
To equip your Treasure Cards, click the golden button with cards on it on the top right of the screen. You can now scroll through your treasure cards and place them in your deck by simply clicking on them. Once clicked, they will appear on the left side of the screen. You can remove Treasure Cards from your old deck if you wish to put them in your new deck.