In regards to The Tempest, what was the Elizabethan attitude towards magic?

If you are interested in magic as a device in
The Tempest specifically (which it seems you are since the question
is in The Tempest group), you should know that Prospero's "magic"
is also symbolicaly linked to the magic or art
of theatre.  Many critics have noted that Prospero the magician is similiar
in how he manipulates and controls the people on his island to a playwright (even
Shakespeare himself) and how he creates and chooses and controls what shall happen in
his play.

So, in this case, for Elizabethans (or anyone
watching the play), the magic of Prospero demonstrates the magic of theatre.  All of the
special effects -- the shipwreck, the charming of the royals after they land on shore,
the infatuation between Miranda and Ferdinand, the masque of the Goddesses -- all of
these things are presented through the "magic" of theatre and are controlled by
Prospero/Shakespeare.

Prospero's curtain speech at the end
of the play, demonstrates the connection between Prospero and the creator of the play
himself when he asks the audience to "free" him with their applause.  He has been
trapped by the magic inherent in the performance, and will only be free to leave at the
audience's command.  This, actually, gives the audience the ultimate magical power, and
connects the character Prospero to the playwright
Shakespeare.

It is interesting to note that some scholars
surmise that this was, indeed, Shakespeare's final play, so strong is the parallel they
find between Prospero leaving his magic garments behind and, potentially, Shakespeare
deciding to leave his play writing behind.  So, for Elizabethans, one of the primary
experiences of magic, in relation to The Tempest, was through
Prospero's theatrical use of magic as a device of the stage.