What is Dredge in Hearthstone?
Hearthstone has many card effects that are common enough that they get their own keyword - a word or two that immediately tells you how the card works. Let's take a look at the Dredge keyword.
Look at the bottom 3 cards of your deck. Put one on top.
Dredge is a mechanic that looks at the bottom 3 cards of your deck and then you choose one of those cards to put at the top of your deck to draw next. This in turn gives you information on your deck order as the cards you don't pick are cards that you know you won't be drawing and when you get to the bottom of your deck, you have an idea as to what you'll draw. Dredge was added in Voyage to the Sunken City and synergizes with various effects that add cards to the bottom of your deck to give you access to them quicker that you normally would.
Keywords that Work Great with Dredge
Dredge has limited direct keyword interaction, however it does have an interesting interaction with Tradeable as you can Dredge a card and then trade away a Tradeable card to draw the card right away. This interaction is fairly situational as it will spend a lot of mana in a turn for a card you would've otherwise drawn next turn anyway, but it is something that you may keep in mind every once in a while.
Otherwise, cards with Dredge won't be available to use right away so any mechanic that helps you survive (Taunt, Lifesteal, etc.) will help you stay in the game until you draw it. Sometimes you may find yourself in a dire situation where you will need to hold out until you draw your Dredged card to turn the tide of the game around.
Beyond keywords, Dredge also has interactions with cards like Holy Wrath and Tentacled Menace as you will know what's on top of your deck in-between the turn you play the Dredge card and your next one.
Playing Against Dredge in Hearthstone
As Dredged cards aren't placed in the hand and aren't usable right away (unless your opponent also draws into the card on the same turn), you will have a turn to prepare a plan for the Dredged card. Certain Dredge cards will also clue you into what your opponent is playing and what the card in question they chose might be. If your opponent plays a Bloodscent Vilefin for instance, you may now suspect a Murloc to be on top of your opponent's deck. This (or any similar effect) may then be factored into your gameplan. If you suspect that your opponent has Dredged a significant card, this is something that you can keep in mind for your next few turns and you will have some time to plan your move out.
As a Warlock, you can use cards like Gnomeferatu, Altar of Fire, or Tickatus to burn a card your opponent Dredges if they don't draw it on that same turn. Mischief Maker can also be used to steal it.
Example Dredge Cards in Hearthstone
Tuskarrrr Trawler is a very basic Dredge card that has no set parameters or after-effects to its Dredge.
Bloodscent Vilefin is a card that can also Dredge anything, but it obviously wants you to use it in Murloc deck as it has a bonus effect if you specifically Dredge a Murloc by making it cost Health instead of Mana.