Is there a quick way to get or buy cards for a specific recipe?

Solution 1:

Deck recipes are popular premade decks that have a decent success rate in the meta. The recipes (and playstyles of the decks) will change with patches and expansions.

To answer your question, there are 4 primary ways to gain cards:

1. Purchase packs with real money.
2. Purchase packs with in game gold (can be earned naturally through playing and completing quests).
3. Play through adventures/story modes (very few cards that are useful in competitive are gained this way).
4. Crafting cards with dust, used for crafting a targeted card.

Based on your current comments, buying deck packs will be your fastest way of getting cards to fill out the recipes (yes it is random, but it's how they get you). Be aware that different cards come from different expansions, so you many need to buy different packs.

You can disenchant duplicates from the packs to gain dust for crafting the cards you need.