There are two fundamental rules in blackjack split strategy: always split aces and eights, and never split fives or tens. Beyond this, whether to split any pair depends on both the dealer's upcard and specific table rules, like whether doubling after split (DAS) is allowed.

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The non-negotiables
In basic strategy blackjack, ace pairs and 8s are always split, regardless of the dealer's upcard. This is because both these splits turn a losing or push hand into two separate hands with good odds of beating the dealer. At the other extreme, fives should never be split, as it's better to hit on a total of 10 no matter what the dealer shows. Tens should also never be split: two tens is already a strong 20, and there's no reliable way to improve this by splitting either card.
Splitting is a way to create two different hands from one, and it always requires placing a second wager equivalent to the original bet. You'll then play each new hand separately, according to the best strategy from that point. It's important to remember that only two cards of equal value can be split, and aces are dealt only one card, or just one. If a blackjack is formed after splitting aces, it counts as a regular 21, not a natural, and pays 1 to 1 instead of 3 to 2.
Where the dealer's upcard matters
For pairs of 2s, 6s, 7s and 9s, splitting turns a board position from 4, 12, 14 or 18, into a 2, 6, 7 or 9. But are those new starting hands enough of an advantage to play? That depends on the dealer's upcard. If the dealer shows 2-6, the house has a poor chance of reaching 17-21, and splitting presses a player bet when the dealer is weak.
On the other hand, if the dealer shows 7-A, the advantage now lies with the dealer, and splitting 2s, 6s, 7s and 9s is no longer recommended.
This does not mean it's always better to split pairs against weak hands, however. There are subtler factors at play, like game protection rules, that can change the decision.