In school, I was always taught that Shakespeare invented new words and that they were later added to the English dictionary. But it's never been clear to me how many of those words were original Shakespeare invention, or slang he simply immortalized by putting them into his plays. Is there a way we can find this out? Google seems a little less helpful than usual.
I recommend reading /u/cdesmoulins's answer to a similar question "If William Shakespeare made up new words for his works, how did contemporary playgoers understand his dialogue?"
Also worth reading is the article "Shakespeare, Word-Coining, and the OED" by Charlotte Brewer, originally published in the Shakespeare Survey journal in 2013. Brewer is a Professor of English at the University of Oxford, and a contributor to the Oxford English Dictionary.
Also of interest is the article "To Be Or Not To Be...Original" by Shakespearean professor David McGinnis at the University of Melbourne, published on the university's website in 2016.
Or, more with a popular audience in mind, you may want to read the article "Coined By Shakespeare? Think Again", published in the Boston Globe in 2013. The article is written by Rachael Scarborough King, now an English professor at UC Santa Barbara.
Consulting these sources, you'll find that while Shakespeare did coin many words, the effect is overstated. This is for several reasons, but one of them is how the Oxford English Dictionary was written and compiled in the 19th century. The editors deliberately included as much Shakespeare as possible as their primary example of Early Modern English usage of words, which led to him appearing to be the "first" user of a word or a definition of a word, when that's not always the case. Most of the current OED still hasn't been updated from its original 1884-1928 publication, but is being painstakingly revised in an ongoing effort begun in the year 2000. As such, many of the Shakespeare "coinages" have been taken out, replaced by earlier-found instances of the same word.
The Boston Globe article quotes a recent study that "concluded that new words attributed to Shakespeare are 'probably overcounted by a factor of at least two'". It goes on to say that, between the final publications of the 1st edition of the OED and the present (still incomplete) 3rd edition, the number of coinages attributed to Shakespeare had already fallen from 3,200 to around 2,000. Meaning, the actual coinages of Shakespeare may only be around the 1,000 mark, and of those, only a fraction are likely to be of his own invention, rather than being the first Early Modern English writer to have happened to write them down. Most would have been readily understood by his plays' audiences, the words being in popular circulation at the time.
There's more to it than that, which cdesmoulins goes over in the answer linked above. It's not that Shakespeare didn't coin many words, but his contribution is certainly exaggerated.
Other answers to similar questions in this sub that might be helpful include /u/Yst's answer to "How did Shakespeare invent words in his plays? Did the audience understand the meanings of the words which he invented?" and /u/texpeare's answer to "Did Shakespeare really "invent" all of the words and phrases he purportedly did, or did his work just contain the first written record of them?".
There is also a section in the FAQ about Shakespeare that may be of use.