The basic assignment operator is "=". Your first inclination might be to think of this as "equal to". Don't. It really means that the left operand gets set to the value of the expression on the right (that is, "gets set to").
The value of an assignment expression is the value assigned. That is, the value of "$a = 3" is 3. This allows you to do some tricky things:
$a = ($b = 4) + 5; // $a is equal to 9 now, and $b has been set to 4.
For arrays, assigning a value to a named key is performed using the "=>" operator. The precedence of this operator is the same as other assignment operators.
In addition to the basic assignment operator, there are "combined operators" for all of the binary arithmetic, array union and string operators that allow you to use a value in an expression and then set its value to the result of that expression. For example:
$a = 3;
$a += 5; // sets $a to 8, as if we had said: $a = $a + 5;
$b = "Hello ";
$b .= "There!"; // sets $b to "Hello There!", just like $b = $b . "There!";