Trivial Picard group of projective variety 
Assume X is an irreducible smooth projective variety. I am trying to prove Pic(X)=0 iff X is a point. 

I am completely new to divisor, so even have no idea for such problem which may be trivial. So is this similar to $\mathbb P^n$? By the way, I am learning this stuff without using sheaves and schemes, so could someone help me without using sheaves? (I have found a similar question with an answer using sheaves, but unfortunately I am not able to understand it.)
Thanks!

If the space isn't a point, fix an irreducible proper subvariety $V$. If this is linearly equivalent to zero, then there's a regular function on $X$ vanishing at $V$ with no poles. But this can't be, because any non-vanishing regular function is constant.
A more concrete approach might be to use the description of divisors on projective varieties in terms of ideals given in section A here, but I admit I haven't worked out the details and don't know if this would be simple.
