I hope I can provide, in so short a space and with my limited knowledge, a useful summary of the subject.
Perhaps the first thing to note about H. P. Lovecraft is that he was raised in the knowledge that his family had once been wealthy and respected but had fallen from that position. Lovecraft was born “to a family that was both well-to-do financially and a part of the informal social aristocracy of” Providence, Rhode Island (Visible World viii). His father died a gruesome death in 1898 of syphilis. In 1904, when Lovecraft was 14, the mismanagement of his grandfather’s estate “forced the family to move... into a smaller house” (ix). He described the knowledge that he had to take a huge step down: “How could an old man of 14 … readjust his existence to a skimpy flat and new household programme and inferior outdoor setting...?”, and contemplated suicide (30). His melancholic personality--I hesitate to call it depression, though many have--surfaced frequently in life and found its expression through his writing; he later wrote, “Life has never interested me so much as the escape from life” (270).
On the subject of Lovecraft's father's death, some scholars have suggested that the feeling of isolation and loss of a father figure also influenced Lovecraft's philosophies about the cosmic smallness and futility of human life. In the last five years of his life, Winfield Scott Lovecraft's mind was destroyed by the disease, and he was confined to Butler Hospital suffering from general paresis and hallucinations. He was declared mentally unfit for reasons of insanity. Throughout his life, Lovecraft wrote that his father died of a stroke from "insomnia and an overstrained nervous system". It is unclear how much Lovecraft knew of the circumstances of his father's death, though he was fully aware that Butler Hospital was a sanitarium. The deaths of several of his cousins when Lovecraft was very young, as well as their somber late-Victorian funerals, are believed to have also contributed to his writing. His mother also died in Butler Hospital, following a series of nervous breakdowns. (Taken from the essay "The Parents of H. P. Lovecraft by Kenneth W. Faig, Jr.)
I will touch only briefly on his mother's over-protectiveness and the fact that Lovecraft lived with his aunts well into his adulthood. His mother insisted that adults should stoop when walking hand-in-hand with little Lovecraft for fear of tearing his arms out of their sockets. She also cried when his long hair was cut for the first time at the age of six.
Because of his weak constitution and “nervous disposition,” Lovecraft struggled in the organized rigor of school. “[A]fter the completion of only his third term” at Hope Street High School, Lovecraft withdrew, and “he was ashamed at his failure to matriculate at Brown University, as his family expected” (ix). He wrote: “Of my non-university education, I never cease to be ashamed... I shunned all human society, deeming myself too much of a failure in life to be seen socially” (35). This shame caused by his failure in academia would resurface in his literature. In his stories, Lovecraft fabricates an alternative authority which defines worth not through formal education, but through an understanding of the uncanny and obscure. In one of his few stories culminating in the defeat of a supernatural horror, The Dunwich Horror, the academics of Miskatonic University who defeat the abomination all study folklore and the occult.
Perhaps the most common themes in Lovecraft’s weird stories are of the inevitable destruction of an individual or civilization through this pursuit of forbidden knowledge. The most developed cultures and the most refined individuals--scientists and scholars, in Lovecraft’s estimation--stand in most danger of these chaotic forces, which the “primitive” and “bestial” parts of society often serve through blasphemous rituals. These researchers, whose work is frequently opposed and dismissed by mainstream science, make up many of the protagonists of Lovecraft’s stories. In this way, he combined his shame about his failing fortunes with his shame about his failure in academia.
Lovecraft lived in Red Hook, New York as an adult, after his marriage. Though he at first wanted to think of it as an old neighborhood rich with the ghosts of the past, it proved instead to be a dirty, raucous, and crude place full of immigrants, and it was torture for Lovecraft to live there. Plenty has been written of Lovecraft's xenophobia. To this I would only add that it must be taken in connection with his love of the past; he saw the uneducated and squalid immigrants as tearing down the stately, grand old America of the bygone era which he loved so much. This is how he described Red Hook: “My guess is that its decay had just set in, owing to the Syrian fringe beyond Atlantic Avenue” (164). Of his leaving, he writes: “It is nearly a full year ago that I left it without a pang to come home to my own--to the clean, white, and ancient New England that bred me” (167).
There has been plenty written of his marriage to Sonia Haft Greene, an immigrant of Russian and Jewish descent. The marriage eventually fell apart. Some have said that Lovecraft's fear of sex and women can be read into this, but Greene is oft-quoted as having described Lovecraft as an "adequately excellent lover," whatever that means. If you're curious about this, I can go more into it, but it has been argued ad nauseam and I'm a little sick of talking about it.
Lovecraft kept up a voluminous correspondence with his friends, many of whom were other writers for Weird Tales. These included Robert E. Howard, Clark Ashton Smith, Frank Belknap Long, August Derleth, E. Hoffman Price, and Donald Wandrei. Their shared communication had a remarkable effect on his imagination and writing.
Among countless others (Lovecraft read a vast quantity), Lovecraft was influenced by Edgar Allan Poe and Lord Dunsany. Since this is more biographical, I'll leave it at that just now.
The quotes were drawn from Lord of a Visible World: An Autobiography in Letters. It's a collection of selections from Lovecraft's own letters, piecing together his description of and feelings about his own life. It's extremely informative.
I welcome any corrections, and deeply apologize if I misread something or used a refuted text.