There are numerous systems introduced for counting the cards when playing Blackjack, but the basic principle is to keep track of the cards so you can calculate the ratio between high and lower cards remaining.
To simplify the things, maybe you won't be able to guess the exact cards, but you will know how many tens are still in the deck, or in the decks, when playing multi-hand.
Some of the counting systems are KO Counting, Hi-Lo Counting, Hi-Opt I and Hi-opt II.
It isn't the higher math, but it is complicated, because you have to count each and every card dealt to you, to other players and the dealer.
Counting systems usually use zero as a starting point for counting the cards. The goal is to get higher chances for predicting if the following card will be low or high.
If your counting result shows you there are more higher cards remaining, you can tell there is a higher possibility for getting the higher cards in following deals. That means it will be more blackjacks, with stronger starting hands, but also that the dealer have more chances to be busted.
According to this, you will bet higher, but you still have to continue counting cards. When the ratio begins to change, you have to adjust your bets accordingly.
It's hard to say which counting system is the best for you. Maybe the bet thing you can do is to try them all, and then decide which one you find more suitable. Of course, some of the systems are made for some particular variations of the game, so you should consider this, also.
Anyway, the main thing is to practice - wherever you can - and to use less complex counting system in the beginning. The advantage differences between simple systems and more complex ones aren't significant, maybe 0.15%, so you don't have to worry that you will miss something with simple systems.
It is highly recommended to start by learning basic systems like KO Count or Hi-Lo Count.
In order of becoming an expert in cards counting, prepare yourself for lots and lots of practicing. There is no other way. You have to practice. Maybe you will need many months, even years to become good enough. You don't have to play, you can practice all by yourself, and you just need a deck of cards and a will. Some experts advise you should make some counting chards to help you practice.