There are more than 30 instances of the word "see" in Macbeth. In this answer format, it is not possible to analyse more than a couple of the most interesting uses of see. You will be able to apply your own analysis to the others. To start with, Duncan tells Ross to deliver to Macbeth his new title of "thane of Cawdor." Ross replies, "I'll see it done." A glance in a good dictionary, like the Oxford Advanced Learners Dictionary, shows that see in this context means "make sure": someone is to make sure that something is done.
Shortly after, Macbeth himself says, "So foul and fair a day I have not seen." Another examination of the dictionary reveals that see in this context means to witness something or some event. Thus, Macbeth has never witnessed such a horrible day--yet. The opposite of this meaning is to reveal. Later, Macbeth says, "Let not light see my black and deep desires." In this context, see has the meaning of to find out: Macbeth doesn't want a metaphorical light to find out, to reveal his black and evil thoughts.
This leads us to the consideration of see in context of personification. In the above instance, light has been personified by giving it human-like characteristics: light will find out, will reveal something. Another instance of see in a personified context occurs when Macbeth says, "That my keen knife see not the wound it makes." Here, the knife is personified and given the ability to perceive the act of slaying Duncan as it happens.
One of the more interesting uses of see is in context of the hallucination Macbeth has in which his dagger appears to hover and float before him throughout quite a lengthy soliloquy, part of which says:
Is this a dagger which I see before me,
The handle toward my hand? Come, let me clutch thee.
I have thee not, and yet I see thee still.
Art thou not, fatal vision, sensible
To feeling as to sight? or art thou but
A dagger of the mind, a false creation,
Proceeding from the heat-oppressed brain?
I see thee yet, in form as palpable
As this which now I draw.
Thou marshall'st me the way that I was going;
And such an instrument I was to use.
Mine eyes are made the fools o' the other senses,
Or else worth all the rest; I see thee still, ....
In this context, see is used in its most common meaning of to perceive by sight, however, the sight is a delusional one of that which does not exist to the perception of anyone but Macbeth. You might therefore say that the meaning here is more akin to the meaning of to imagine. In a similar vein, Macbeth later calls on seeing through a 6th sense, "As they had seen me with these hangman's hands," which can also be understood as to imagine. As you examine the others, pay attention to the eventual use of "see" by Macduff and Malcolm who take over from Macbeth the emphasis on "see."
Hail, king! for so thou art: behold, where stands
The usurper's cursed head: the time is free:
I see thee compass'd with thy kingdom's pearl,
That speak my salutation in their minds;
Whose voices I desire aloud with mine:
Hail, King of Scotland!
Of this dead butcher and his fiend-like queen,
Who, as 'tis thought, by self and violent hands
Took off her life; this, and what needful else
That calls upon us, by the grace of Grace,
We will perform in measure, time and place:
So, thanks to all at once and to each one,
Whom we invite to see us crown'd at Scone.