How do the strong acids dissociate?
This is a little tricky. I would argue that only the first proton dissociates completely and should be considered "strong" - using the rules for writing net ionic equations, where we only dissociate strong electrolytes, this would meant that we would write:

$\ce{H2SO4 + 2KOH -&gt; 2H2O + K2SO4}$

$\ce{H+ + HSO4- + 2K+ + 2OH- -&gt; 2H2O + 2K+ + SO_4^{2-}}$ - here only the first proton dissociates completely

Canceling out spectator ions gives:

$\ce{H+ + HSO4- + 2OH- -&gt;2H2O + SO_4^{2-}}$

Your teacher (or whoever is giving you that answer) is dissociating the second proton as well, to give:

$\ce{2H+ + SO_4^{2-} + 2OH- -&gt;2H2O + SO_4^{2-}}$

Which becomes:

$\ce{H+ + OH- -&gt;H2O}$

There are a few reasons why they might do this, but I would argue that the 1st approach (which only dissociates the first proton) is best because it more accurately reflects what is happening, in the sense that $\ce{HSO4-}$ is a weak electrolyte. This will become important later when you study acid-base equilibria.

In general, you dissociate protons from acids as if they were regular metal cations - just "pull them off" and don't forget the positive charge. For polyprotic acids, the first proton is strongly acidic, or dissociates completely, but the other protons are not. There might be exceptions to this rule but I can't think of any off the top of my head.