If [tex]p[/tex] is true, then [tex]\sim p[/tex] is false, which in turn means [tex]\sim(\sim p)[/tex] is true.
If [tex]p[/tex] is false, then [tex]\sim p[/tex] is true, and so [tex]\sim(\sim p)[/tex] is false.
So, because [tex]p\equiv\sim(\sim p)[/tex] in both cases, the statement is a tautology (always true).
If you were to put this in a table, you would have one column each for [tex]p,\sim p,\sim(\sim p)[/tex]. In the first column ([tex]p[/tex]) you can think of [tex]p[/tex] as an independent variable that can only take two values, true and false. In the next column ([tex]\sim p[/tex]), you would negate the value in the previous column. And so on.
It should roughly look like this:
p ... ~p ... ~(~p)
T ... F ... T
F ... T ... F
