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.
Between the two, 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 being 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 updated in an ongoing effort since 2000. As such, many of the Shakespeare "coinages" have been taken out, replaced by earlier-found instances of the same word.
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.
That’s a great question my students ask often when I talk about his vocabulary. This answer has multiple parts:
sometimes the words just make sense the first time you hear them. He combined words into compound words often such as “eye balls” or “upstairs”. English speakers were familiar with both eyes and balls in the vernacular so combining them just makes sense. He made variations of words like going from the pre-existing word alone to create lonely.
Sometimes they didn’t understand them. This is a broad stroke because we don’t have any extant reviews from the illiterate viewers of his plays because they simply couldn’t write them. We know his plays were frequented by members of all education levels. Shakespeare’s plays are spoke. So rapidly that we have to assume sometime it just didn’t land. To combat this, plays had a dumb-show before them where the plot of the play would be acted out in pantomime over a couple minutes so people knew what would happen.
Sometimes people learned over time. Plays from around this period were performed in repertory over years on and off. After seeing something a couple times, you could start to learn. All it takes is one guy to use a phrase then it spreads. “Tough love,” “what’s done is done” are examples or expressions and not necessarily individual words but the system is the same. This is analogous to how humans acquire language in infancy— we hear our parents repeat things and it just clicks after a while.
The works of Shakespeare are some of the most widely read, performed, and acclaimed of the past 400 years. His works have personally enriched my life and so many others and it’s his language for me. He can reach into my soul and express the deepest parts of my heart in words I could never have, and by doing so, has shown me myself.
For further reading and sources see the Bevington edition of the Complete Works of William Shakespeare. His introductions discuss the dumb show, what play performances were like, etc.