How to make a boolean variable switch between true and false every time a method is invoked?

value ^= true;

That is value xor-equals true, which will flip it every time, and without any branching or temporary variables.

Without looking at it, set it to not itself. I don't know how to code it in Java, but in Objective-C I would say

booleanVariable = !booleanVariable;

This flips the variable.

Just toggle each time it is called

this.boolValue = !this.boolValue;

Assuming your code above is the actual code, you have two problems:

1) your if statements need to be '==', not '='. You want to do comparison, not assignment.

2) The second if should be an 'else if'. Otherwise when it's false, you will set it to true, then the second if will be evaluated, and you'll set it back to false, as you describe

if (a == false) {
  a = true;
} else if (a == true) {
  a = false;
}

Another thing that would make it even simpler is the '!' operator:

a = !a;

will switch the value of a.