In some regards, very accurate; in others, events and characters are completely made up.
The basic facts of history are, for the most part, followed closely; however, the show is oft to make insinuations about characters' lives or completely invent personalities for them.
Some basic facts of history, however, were not that carefully noted. Examples of a few revealing mistakes: (1) the impending death of Pope Alexander is mentioned in the first episode of season 1 when, in actuality, Pope Alexander VI died six years before Henry VIII's coronation; (2) there is mention of an Orsini cardinal having been elected Pope in the second episode of season 2 when, in actuality, there were no Orsini Popes during the 1500s.
There is no historical evidence that Mark Smeaton was a homosexual; Smeaton's depiction as such in the series stems from a contemporary historical theory that he was chosen as a "patsy" because, by medieval standards, he lacked masculine characteristics and so would have been seen as feminine (and therefore weak) by a jury, which would have lessened their sympathy for him. Similarly, there is no evidence that either George Boleyn or Thomas Tallis were homosexuals, either; the real George Boleyn was regarded rather positively by his contemporaries as an exceptionally well-spoken individual who was also used in addition to his sister as a pawn in their father's political power-plays. George's closing statement at his own trial was so convincing that pubs had 10:1 odds in favor of his acquittal.
Additionally, for the sake of time and keeping the cast of characters to a minimum, some characters are composites, and timelines are truncated. Henry's sisters Mary and Margaret are compiled into the single Margaret Tudor, with the majority of her story arc coming from the life of Mary Tudor; the writers chose the name Margaret so as to avoid viewer confusion with Henry's daughter, Mary Tudor (who was in fact named for her aunt). "Margaret's" storyline is also heavily truncated; she lived much longer than is depicted on the series, and was in fact married to the King of France (not Portugal, as shown) for over a year, until his death from natural causes. ("Margaret" is depicted killing him on the series both for dramatic effect and to hasten the storyline of her marriage to Brandon). Mary was married to Brandon for several years (not months, as depicted on the series) and the two had children together, becoming the grandparents of Lady Jane Grey, the fourth Tudor Monarch, often regarded as a usurper instead of a monarch.
A similar dramatic tool is used in Season 2 and 3, when the character of Norfolk was written out of the series and much of his role in events was written into either Brandon or Thomas Boleyn's characters.