It’s perfectly acceptable today to use contractions. In fact, throughout the history of English it’s usually been fine. But there was a time…
Contractions go back at least as far as Old English, which included “nis” (ne is, meaning “is not”), naes (ne waes, meaning “was not”), nat (ne wat, meaning “does not know”), and plenty more.
Fast forward a few centuries and you’ll find them used extensively in Shakespeare. “But he’s an arrant knave” is from Hamlet, and All’s Well That Ends Well is even a title. Without counting, it certainly appears that contractions might be less used now than in the past, when people had the options of contractions such as “’tis,” “‘twere,” and even double-apostrophe-contractions like “ha’n’t” and “sha’n’t”.
But then came the 1700s. Prominent pundits of the day such as Alexander Pope and Jonathan Swift began suggesting that contractions were unsuitable for print — and probably not particularly welcome in speech either. And it worked; by the end of the 1700s all the authorities on English agreed that if you used a contraction in writing it was a sign of…well, nothing good.
It wasn’t until the early twentieth century that contractions began to make a comeback. There was a popular guide to English usage in the 1920s that included contractions, and the author (Henry Fowler) suggested that there was nothing wrong with them. It’s not entirely clear how the change happened, but it very well might have been because of Mark Twain. His books were enormously popular in the late 1800s, and taking just one example — Tom Sawyer — he used “won’t” 58 times compared to “will not” once, and “don’t” 223 times compared to “do not” just, again, once. (It’s amazing what ridiculous trivia you can look up on the internet.)
Modern English usage doesn’t seem to be generating new contractions — at least not generally ones that include apostrophes to show where the missing letters were. Not sure why that is either. But it shouldn’t be too hard to figure out if you’ll put your minds to it.