How does one go about implementing this into their games?

Swim gave some advice on one of his streams which sounds like good advice, but I'm unsure how to use it properly. He said; in the lower tiers like plat and below the game is about getting the most value out of your cards. Like attacking when you have a good opening, but in the higher ranks value starts taking a back seat to probability. For example; there is an opening you can use to deal some good damage to the enemy. Now you have to ask yourself; what is the probability he has something in hand that could either stop it or put you at a disadvantage in the next round? If so. What is it? How could you play around it? If you do play around it; will it make a difference?

He said that's why you sometimes see master level players making moves that don't seem to provide much value at first glance, but that's because they are most likely trying to either play around something they think the other guy has, or they are trying to give themselves an advantage in the next round or two.

Well I'm reaching that point where you have to shift from value to probability because I'm stuck at plat 1. How do you make that change in mindset? 

I guess a large part of it is knowing your matchups and regions, and using that information to deduce which cards would punish you.

I see mogwai skipping a lot of attacks/turns to burn the enemy mana when they try to bluff or to greed their resources, you need to think, sometimes your opponent will skip their turn if you have challengers on offense, cause he doesn't want to get challenged, and play those units after you attack, you can abuse that to make them lose mana sometimes..

btw I am silver (don't have much time to play.. :( ) but I got to legend once in HS and I watched almost every mogwai video from launch :D, just that I don't play much ranked.. so take my advice with care.. it's just something I noticed mogwai and swim do a lot.

Look at their mana, what can the enemy play that can screw you up..

pay more attention when you have the "end round button" and the opponent have a lot of unspent mana.

I have not heard the exact advice you're describing from Swim's stream, but as you're describing it I would argue that it's actually pretty bad advice.

Playing for value vs. playing for tempo (or, even skipping a turn to try and bait out your opponent's threats) is a core part of the strategy of just about every CCG. And the question of when to maximize value of your cards has to be done in the context of the match. Imagine you're playing a midrange deck and your opponent is playing a control deck. In that case, your opponent probably has better late game cards, so if you spend the whole game waiting for opportunities to maximize value, you'll just lose by giving your opponent time to get their better cards online. This is the idea of knowing when you're the aggro players and when you're the control player in the context of the match (there's a widely popular article from about 20 years ago on this very topic in MTG - "Who's the Beatdown").

So, the suggestion that the game is about maximizing value at or below Platinum ranks suggests that there's some fundamentally different meta game at lower ranks. Specifically, it suggests that the meta game is all about control decks, which will naturally want to maximize value as a means of winning the game. The most generous interpretation of the advice being given is that Swim is saying that you can get away with just maximizing card value at or below Platinum rank (effectively saying that you can get away with playing the game worse), which seems to suggest that he thinks everyone at or below Platinum is either bad at the game or playing random, off-meta decks.

As @thazud said, the most important thing you can do is know what the meta game looks like and what your opponent's strategy is based on the regions/champions they're playing. From there, you can easily decide at a high level what your strategy for the match is - are you the aggro, or the control player? This is the single most important thing you can do to improve win rates, as knowing the broad strokes of your strategy going into a match informs your mulligan decisions.

Going beyond you can guess at which cards they might have that can screw you over, and gauge the likelihood of whether they have them in their hand over time. (E.g. if you're "the aggro player" in the match, and your opponent skipped a good opportunity to wipe your board with The Ruination, it may be an indicator that they don't have the card in hand and that it's safe to invest more in the board in order to close the match quickly.) If you're trying to get to a really serious expert level, you can try to develop hand-tracking skills (basically, monitoring which cards are lingering in their hands turn over turn to guess at what they are). This is something that popular Hearthstone decktrackers do for you, but it looks like Mobalytics doesn't have that feature.

First, at the start of the game, you need to figure out what is your win condition and what is your opponent's one. 
If the opponent on average can reach their win condition faster then you can, then usually you have to play from a control position and do your best to deny their win condition, even if your deck is build to be aggressive. 

Playing as agressor: There is almost no reason to slowdown. Every turn wasted is a turn your adversary will be closer to their win condition.
The exceptions are to:
1- Protect one Key Card from being removed;
2- Bait a Keycard from your opponent into a bad situation;
3- Delay a given combo due not having enough mana to pull it off or the pieces are not assembled yet;
4- You already have Lethal next turn;
5- etc;

Playing as control: You want to slowdown as much as possible. If the other player passes a turn without playing anything, always consider the possibility to end the turn right away, even if that means losing the attack token or waste mana.

Game example: Shadow Island(Elise + Kalista) vs Bilgwaters/Piltover (Heimerdinger + Twisted Fate)

Its Turn 4. You are the agressor and have the attack token, 4 mana and no spell mana. Adversary has 6 mana (4 + 2 spell mana) and also 5 cards on his hand. 
Hand: Vile Feast, Crawling Sensation, Kalista, Elise, Hapless Aristocrat, Brood Awakening
Board: Spiderling + Spiderling + Spiderling. Nothing on the other side.

What do you do? Take some time to answer those questions before clicking the spoiler tag:
1- Do you open attack? If not, which followers you play first if any? 
2- Assume he passes his turn back to you after being attacked or a follower was played, what do you do now?
3- What cards are you expecting he may play on T4?
4- What is the best next T5 play he may do?

Answer:

Quote From Vincent3383

Well I'm reaching that point where you have to shift from value to probability because I'm stuck at plat 1. How do you make that change in mindset? 

I'm not really sure how to help you--for me, that IS this game.  Every move, including just passing, has upsides and downsides to both players, and whichever player successfully judges which moves will create the biggest differential will probably win.  There was actually an interesting Runeterrable podcast last week with FreshLobster about this: he's actually a poker player who got into CCGs, and the hosts were commenting about how this just lets him see the game differently and how he doesn't have to unlearn habits like spending all your mana every turn.

One thing that might help you is playing different meta decks, so that way you get a better feel for their strengths and weaknesses.  E.g., if you play endure spiders, you might be able to better appreciate how important it is to level Kalista and how critical removal is if they have another 2 mana for Haunted Relic.