How does Macbeth becoming king affect Lady Macbeth? Why does she want him to become king so badly and what is she going to gain from this happening?

Lady Macbeth wants Macbeth to become king because she is very ambitious and power-hungry.  When he arrives home after she reads his letter, she addresses him by saying, "Great Glamis, worthy Cawdor, / Greater than both by the all-hail hereafter!" (1.5.62-63).  If Macbeth becomes "greater," then so shall she, as his wife.  Just as he will be king, she will be queen.  Further, it is possible that she hopes to rule through him, as her...

Lady Macbeth wants Macbeth to become king because she is very ambitious and power-hungry.  When he arrives home after she reads his letter, she addresses him by saying, "Great Glamis, worthy Cawdor, / Greater than both by the all-hail hereafter!" (1.5.62-63).  If Macbeth becomes "greater," then so shall she, as his wife.  Just as he will be king, she will be queen.  Further, it is possible that she hopes to rule through him, as her immediate response to his letter (and their subsequent conversations in Act One show that she is -- at least initially -- the dominant partner in this relationship.  She wants him to

Hie thee hither,
That [she] may pour [her] spirits in [his] ear
And chastise with the valor of [her] tongue
All that impedes [him] from the golden round [...]. (1.5.28-31)

She plans to murder Duncan in order to smooth Macbeth's path to the throne because she is afraid that Macbeth is too compassionate and loyal to do it himself.  Further, Macbeth loves her and seems like the kind of king who would trust his wife as his closest adviser.  He does call her his "dearest partner of greatness" and his "dearest love" (1.5.11, 67).  Thus, she has many reasons to think that her own power will be monumentally increased, her own ambition satisfied, by Macbeth's becoming king.

Once Macbeth does become king, however, she doesn't seem nearly as pleased as she expected to be.  She says, 

Naught's had, all's spent,
Where our desire is got without content.
'Tis safer to be that which we destroy
Than by destruction dwell in doubtful joy. (3.2.6-9)

In other words, they have gotten what they wanted (to become king and queen) but they are not happy.  She thinks it is better to be dead than to live unhappily as they do.  Further, Macbeth no longer seems to be consulting her in important matters; he orders the murders of Banquo and Fleance without her input and purposely keeps her in the dark about it.  He even goes so far as to give her instructions about how to treat Banquo at their dinner party (a party he knows Banquo will not be alive to attend).

By Act Five, Lady Macbeth seems to realize that she has created a monster in Macbeth.  He now murders innocents indiscriminately, and she feels all the guilt of goading him into that first kill.  Now, she sleepwalks and cries, "who would have thought the old man to have had so much blood in him? [....]  The Thane of Fife had a wife.  Where is she now?  What, will these hands ne'er be clean?" (5.1.41-45).  She clearly feels very guilty about the murder of Duncan as she imagines that she still cannot clean his blood from her fingers; moreover, she laments the deaths of Macduff's wife and children, murders ordered by Macbeth that were nothing but spiteful and cruel.  He has become a tyrant, and she is sorry for it.  The fact that she later takes her own life also seems to convey her guilt and disappointment.