I can't understand logical implication I just started studying logic (high school)
anyway...for the truth table of logical implication

If sentence $A$ is true and $B$ is true then $A\implies B$ is true.

does that mean if $A$ and $B$ are both true
then there is a way to prove $B$ is true from $A$,
always?

the same for if $A$ is false can you get anything either True or false proved from this $A$?
As a logical proposition, the material conditional $A \implies B$ is a very weak one: as you've noticed, it's very easy to satisfy it just by accident. In fact, this happens whenever $A$ is false, or whenever $B$ is true. Thus, merely observing that $A \implies B$, for some specific $A$ and $B$, says very little.

Instead, the usefulness of implication lies in the fact that, precisely because of its weakness, it is often possible to assert $A \implies B$ as a universal statement (either an axiom or a provable theorem) that holds for any valuation of any free variables mentioned in the propositions $A$ and $B$.

For example, consider the statement: $$x &gt; 2 \;\land\; x \text{ is prime} \implies x \text{ is odd}.$$ Merely observing that this statement holds for some $x$ says very little &mdash; there are plenty of numbers for which it is trivially true, either because they are odd, or because they are not primes greater than 2. What makes this statement useful is that we can prove that it holds for all $x$ &mdash; there isn't a single number which would be greater than 2 and prime, but not odd.
This illustration of logical implication might help:

a) When you truly understand logical implication,
b) then you’ll be a happy person.

You may be a happy person for other reasons. But if you’re unhappy, then certainly you don’t truly understand logical implication.  :-)

Truth table:
a  b  a⇒b
F  F  T
F  T  T
T  F  F
T  T  T

I hope this somewhat intuitive example helps.