In Erlang, when do I use ; or , or .?

I like to read semicolon as OR, comma as AND, full stop as END. So

foo(X) when X > 0; X < 7 ->
    Y = X * 2,
    case Y of
        12 -> bar;
        _  -> ook
    end;
foo(0) -> zero.

reads as

foo(X) when X > 0 *OR* X < 7 ->
    Y = X * 2 *AND*
    case Y of
        12 -> bar *OR*
        _  -> ok
    end *OR*
foo(0) -> zero *END*

This should make it clear why there is no ; after the last clause of a case.

Comma at the end of a line of normal code.
Semicolon at the end of case statement, or if statement, etc. The last case or if statement doesn't have anything at the end. A period at the end of a function.

example (sorry for the random variable names, clearly this doesn't do anything, but illustrates a point):

case Something of 
    ok ->
        R = 1,     %% comma, end of a line inside a case 
        T = 2;     %% semi colon, end of a case, but not the end of the last
    error ->
        P = 1,     %% comma, end of a line inside a case
        M = 2      %% nothing, end of the last case
end.               %% period, assuming this is the end of the function, comma if not the end of the function

You can think of it like english punctuation. Commas are used to separate things in a series, semicolons are used to separate two very closely related independent clauses[1] (e.g. the different cases of the case statement, function clauses of the same name and arity that match different patterns), and periods are used to end a sentence (complete thought).

1. Or to prove you went to college. "Do not use semicolons. They are transvestite hermaphrodites representing absolutely nothing. All they do is show you've been to college." -- Kurt Vonnegut

The comma separates expressions, or arguments, or elements of a list/tuple or binary. It is overworked.