How did the Renaissance influence 16th century English literature?

In the sixteenth century, men such as Sir Thomas Elyot advocated for educating students in Latin and Greek, bringing the Italian Renaissance squarely into English life. The Renaissance, which means rebirth, brought classical literature from Ancient Greece and Rome back to the forefront of European intellectual culture and initiated a shift from wholly Christian motifs to literature that blended Christian and secular humanist worldviews. Humanist worldviews moved some of the emphasis in thinking away from celebrating God, instead focusing on man as God's glorious and crowning creation.

We see the influence of the Renaissance in England on Sir Thomas More's Utopia, which brought the term "utopia" into the literary lexicon, and on the sonnets of Sir Thomas Wyatt, who introduced England to the Petrarchan sonnet and translated many of Petrarch's sonnets into English, while composing his own as well.

Shakespeare, of course, comes to mind as a person whose output was deeply influenced by his knowledge of classical sources, such as Ovid, which helped him produce Romeo and Juliet and A Midsummer Night's Dream, as well as his knowledge of classical history, which appears in plays such as Julius Caesar. Shakespeare also transmitted an influential outlook on life that celebrates the interiority and wonder of the human individual. Hamlet, for example, because of his self-reflection, has been called the first modern hero.

The influence of the Italian Renaissance on 15th-century English literature is extensive and far-reaching.  I'll cite two specific examples of its influence for you.

First, English writers were influenced by the Italian sonnet form of poetry.  They imitated Petrarch's sonnet form and created sonnets using the Italian form themselves.  Then, English writers built on the form to create Spenserian sonnets and Shakespearean sonnets. 

Second, the Italian Renaissance involved a rediscovery of Ancient Greek and Roman tragic drama.  Thanks to the influence of the Renaissance dramatists and thinkers, Shakespeare and other writers also knew of and studied classical tragedy, and then wrote tragedies themselves.  In short, without the Italian Renaissance, Shakespeare never writes Hamlet, Macbeth, Romeo and Juliet, etc., in the form that he does.

In its broadest sense, the Renaissance was a reawakening of the spirit after the restrictive and God-focused Medieval period. The Renaissance brought a sense of freedom to all aspects of life in England, including philosophy, art, and writing. Instead of the focus being strictly on God and the Catholic Church, Renaissance artists and thinkers began to contemplate the relationship between man and God. This allowed writers, in particular, to explore themes they had never been able to examine before this rebirth.

New forms of poetry and writing were developed during this period, but it is Shakespeare's writing which inspired the most change and therefore demonstrated the most influence from the Renaissance. Because plays were so popular and so accessible, everyone from the lowest peasant to the highest nobleman was exposed to his work and therefore to his new way of thinking.

Because England's social hierarchy was no longer so rigid (as it was during the Middle Ages), Shakespeare and others were free to allow every character on stage to experience inner conflict and human suffering. Until now, the religious and noble were exempt from such demonstrations of humanity. Kings and commoners now all suffered the pangs of guilt, the complexities of love, and the torments of indecision (think Hamlet).

Another change in the writing of the Renaissance is the depiction of completely developed, multidimensional characters from all stations of life. No longer were some (royal and religious, in particular) exempt from fallibility and flaws. Shakespeare portrayed them as humans rather than as mere representatives of their classes.

Finally, Shakespeare was able, because of the renewed interest in classical literature, to utilize Greek and Roman mythology into his plays. Such works had been repressed by the Catholic Church during the Middle Ages, but these colorful and useful characters and stories could now be used in everyday life because Shakespeare and others could reference them in their writings. (Perhaps you have read a Shakespeare play and noticed all the allusions to these historical and literary figures.)

Other genres of literature as well as art, music, philosophy, and even science flourished during the English Renaissance; however, in the literary world, there is no better example than Shakespeare of the impact this rebirth had on English literature. 

How did the Renaissance influence English literature?

Well, the word "renaissance" means literally, "rebirth".  In this time period in England, many new things were coming about in areas of art, philosophy, religion, music, etc.

For literature, the lyric poem came about, and the sonnet was invented and perfected by Shakespeare and Spencer.  Shakespeare also did something else that hadn't been done before, and that was to combine the elements of tragedy and comedy into one play...namely Romeo and Juliet, but all of his tragedies have elements of comic relief in order to help the audience absorb the horror they had just witnessed and relax a little from the edge of their seats.  Take the Porter in Macbeth who, in his drunken state, is on his way to answer the knocking at Macbeth's castle gate but pretends that he is answering the gate of Hell just after Duncan's gory murder.  There are silly scenes with Rosencrantz and Guildenstern and with the grave diggers in Hamlet for the same reason.

I'm sure there are others, but this is a good jumping off place--the lyric poem, the sonnet, and the transition of play writing.

Good Luck!