There are a plethora of articles online detailing this now. I'll list some of them now.
This blog details some similarities:
...the movie does draw extensively on Scientology and its past. Anderson finally admitted outright a couple weeks ago that he based the charismatic leader Lancaster Dodd (Philip Seymour Hoffman) on Hubbard, adding that much of the film “related to the early days of Dianetics.”
It goes on to list some of the similarities in some detail, but just choosing the "topic headings", it covers:
“Processing”
Scientology centers around a procedure called “auditing,”
which uses probing questions and other techniques to identify
traumatic memories (called “engrams”), to drain them of their power.
Dodd’s spiritual practice, called The Cause, employs similar
techniques.
Books
Lancaster Dodd, like L. Ron Hubbard, spreads his word primarily
through his books.
Family life
Just like Lancaster Dodd, L. Ron Hubbard had multiple
children with multiple wives, and many of his ex-wives went on to
become his critics.
“A writer, a doctor, a nuclear physicist, a theoretical philosopher.”
Dodd, like Hubbard, likes to tout academic credentials, though neither
of the men’s claims seem to hold up to scrutiny.
“Man is not an animal.”
One of the ideas Dodd returns to most
frequently is his belief that “Man is not an animal.”
Reincarnation
Dodd never lays out his full theology in The Master, but we do get
bits and pieces. The Cause, like Scientology, promotes the idea of
reincarnation, believing that through “processing” people may recall
past lives.
Move to England
In The Master, we last see Dodd sometime later in the 1950s, when he
has relocated to Britain. (The timeline isn’t obvious.) There, he
works in a mansion on a hill in the English countryside. Hubbard
similarly moved to the English countryside, in 1959, where he set up
shop in a Sussex mansion called Saint Hill Manor.
Miscellany
Some of the similarities between Hubbard and Dodd are more incidental.
For example, there’s a scene in The Master in which Dodd goes out to
the desert to play a game of “Pick a Point.” The game involves
choosing a point on the horizon and then racing there as fast as you
can, even if that means riding a bit recklessly. The suspense of the
scene echoes an incident in the life of L. Ron Hubbard, who crashed a
motorcycle in southern Spain in 1974, suffering a broken arm and
several broken ribs.
....Both men love boats, too...
I think that blog covers all the major similarities, but do a simple google search for the cause Scientology similarities and you will be inundated with information.
