Edward de Vere composed, directed and acted in plays in the Elizabethan period. He managed a troupe called the ‘Oxford Boys’ and was embedded in the theatre community. He would also have had access to court and the necessary education to write at length on the subjects present in Shakespeare’s plays.
His status as a nobleman in Elizabethan England would have meant that he could not be seen putting his name to written works. Aristocrats were not expected to write. They could manage troupe and finance performances, but writing plays was not considered a worthy pursuit of the nation’s noble stock.
His writing style closely resembles Shakespeare’s. The pair are the only two Elizabethan poets to use a six-line pentameter stanza. 
De Vere’s nickname was also “Spear Shaker”. It stemmed from his athletic prowess in tournaments and his coat of arms, which featured a lion brandishing a spear. He also lived near Shakespeare on the banks of the River Avon in Bilton Hall. Therefore, he would have been familiar with the Warwickshire area and the local landmarks that litter Shakespeare’s plays.
The chronology also lines up. De Vere published several poems under his own name, then stopped. Soon afterwards, Shakespeare began publishing work under his name. The evidence is circumstancial, but when considered alongside everything else, it begins to paint a picture of the real author.
Hamlet is Autobiographical
The story and narrative arc of Shakespeare’s masterpiece align with events and relationships in Oxford’s own life. Lord Burghley, Queen Elizabeth’s chief minister, is strikingly similar to Polonius. His children, Robert and Anne, bear resemblance to the characters of Laertes and Ophelia.
Oxford was unhappily married to Anne and believed she had been having affairs behind his back (so much so that he doubted his paternity of their daughter). He, therefore, becomes Hamlet. Hamlet and Oxford are both athletic and poetic. Both loved the theatre, both were captured by pirates, both had fought in sea battles and both had a trusted friend named Horacio (Horace Vere was Oxford’s closest cousin). In one scene, Hamlet tells Polonius, "Conception is a blessing, but not as your daughter may conceive”, a clear nod to his paternity suspicions.
Given that Hamlet was such a clear expose of Elizabethan court, the fact that Shakespeare wasn't executed for treason indicates that many in the upper-echelons of Elizabethan society likely knew that he wasn't the play's author.