Below are a couple of guides to get you started, but if you know of any others, or if you are planning on writing one yourself, let us know!
Tips for Hearthstone by Mike Donais - This blog covers some basic concepts in deck building and gameplay.
Official Guides - These official guides will get you started with the basics.
How to Play
Basics and Play Tips
Facebook Getting Started Guide
Trump Teachings - Introduction
Trump Teachings - Board Control with Mage Basic Deck Guide
Trump Teachings - Mana Efficiency with Druid Basic Deck Guide
Trump Teachings - Fearless Tapping with Warlock Basic Deck Guide
Trump Teachings - Fearless Hitting with Rogue Basic Deck Guide
Trump Teachings - Favorable Trading with Shaman Basic Deck Guide
Trump Teachings - Card Advantage with Priest Basic Deck Guide
Trump Teachings - When to Face with Hunter Basic Deck Guide
Trump Teachings - Weapons Hold with Warrior Basic Deck Guide
Trump Teachings - The Long Game with Paladin Basic Deck Guide
New Player Guide - by Kripparrian
New Players – These guides start from the basics, including commonly used game terms, what cards to choose, and why to choose them.
Tips for Those Just Starting Out by Daerbon
Hearthstone 101: Beginner Handbook by TheWaterBoiler and Rafajafar
Hearthstone Overview: Heroes, Common Effects and Exclusive Cards by Vincent
The Beginner’s Guide to Hearthstone by Khalanil
Unofficial Hearthstone Glossary by Raz
A Beginner’s Guide to HS Terms by Hayl_Storm
A Beginner’s Guide to Hearthstone Mechanics by MoonBear
Hearthstone for Beginners (Guide and Resource) by cgmcnama
An Updated Guide to Deck Types by Hearthstoneplayers.com
Constructed Deck Building – These guides are for players who know the basics, and want to try something new.
Aidan's Free To Play Budget Decklists by Aidan
Hearthstone: How To Build A Deck by Vlad
Starting Stone #1: Six Steps to an Ultimate Deck by curi
Starting Stone #2: The Best Free Neutral Cards by curi
Deck Builder by Hearthhead
Crafting – These guides are for when there is a specific card you want, and how to determine which cards to disenchant.
Beginner's Guide to Crafting Legendaries by Hearthstoneplayers
Hearthstone Crafting Guide by Messiah
Netdecking 101 by Puffin
Card Advantage by Ben Chapman
A Guide to Odd Hearthstone Mechanics by Jagos
How to Avoid Overextending
How to Hit Legend in Hearthstone by Zhandaly
Have a guide of your own to share with the community? Send it to Daxxarri@blizzard.com.