FYI, the word "assassin" was used prior to Shakespeare. It was "assassinate" that Shakespeare coined, which is fairly easy to interpret provided that you know the word "assassin" and recognise the verbal suffix "ate".

The word assassin actually derives from a fanatical group of radical Islamists in the 11th century who were known to assassinate political figures, particularly crusaders, and before doing so they would eat some hashish (hash, or cannabis). They became known as hashishins which means "hash eaters". Hashishin eventually became assassin in late medieval English.

Context is key.

GLOUCESTER: Now fetch me a stool hither by and by. Now, sirrah, if you mean to save yourself from whipping, leap me over this stool and run away.

SIMPCOX: Alas, master, I am not able to stand alone: You go about to torture me in vain.

Gloucester is talking to a man who claims to have been blind and then have his sight miraculously restored. Gloucester doesn't believe the man and is standing over him with a whip in his hand. Even if you've never heard the word before, watching or reading the play, you can figure out that "torture" means "hurt" of some kind.

Here is a handy guide which contains a list of words Shakespeare first used, and links to the scenes in which those words appear. If you read the surrounding context, you can figure out the meaning of the word easily enough. The same way a modern reader can figure out the meanings of the archaic, unfamiliar words.

Edit: As to why Shakespeare invented a new word. I don't know. Why does any new word get invented? I suppose because the sound and feel of the new word best conveys the true meaning the author is trying to convey.
Shakespeare was also a poet, remember. And poets often have to modify words.
"You go about to torture me in vain," is Iambic Pentameter, for example. "Hurt" or "Whip" wouldn't fit the meter.

Hi, you may be interested in a few earlier threads...

• If shakespeare invented thousands of words, how did people watching his plays have any idea what people were saying? and How did Shakespeare invent words in his plays? Did the audience understand the meanings of the words which he invented? featuring /u/Yst

• Shakespeare is credited for inventing many common words we use today. If he was the first one to use them (with no definitions or explanations for what they meant in the text) how did the common folk derive their meaning and use them so often that they're still a part of our vernacular today? featuring /u/texpeare

The number of words 'created' by Shakespeare is aggressively overestimated. In fact, the OED has falsely credited first uses to Shakespeare. I should also note that Shakespeare is the most widely quoted author in the OED. We like to think Shakespeare invented all these words--he didn't. Sure, he may have coined some of them, but not the thousands he's credited with.