LCD Weather Station - "Press To Start" Function
As Majenko points out in his comment, a couple of your if statements have the assignment operator (ie. =) whereas you are actually after the comparison operator (ie. ==).

if (buttonState = 0)


should be:

if (buttonState == 0)


And

if (buttonState = 1) {


should be:

if (buttonState == 1) {


When an assignment is used, the if statement will execute if the value being assigned is a non-zero. For more information see Using assignment as a condition expression? over on Stack Overflow.