How to represent, using a Venn diagram : complement of A is included in B? It seems easy to me to represent : 


*

*A is included in B


and 


*

*A is included in complement of B. 


But I can't find a way to represent : complement of A is included in B. 
 A: In the following, I am following this method of using Venn diagrams to represent claims, i.e. where shading an area means that that area is empty.
So, for example, to represent that $A$ is in $B$, you do:

That is: by shading the area that is in $A$ but outside $B$, any $A$ that exists is forced to be in the intersection of $A$ and $B$, i.e. it has to be in $B$ as well. So: $A \subseteq B$
Likewise, to represent that $A$ is in the complement of $B$, we have to rule out anything that is in $A$ and also in $B$, i.e. we shade the intersection:

Note that any $A$ is forced outside of $N$, and inside the complement of $B$. So: $A \subseteq B^C$
OK, so now we come to your claim that the complement of $A$ is in $B$.  Well, for that you cannot have anything outside of $A$ that is also outside of $B$. So, you can draw this by shading that very area: the area outside of both $A$ and $B$:

Note that anything that is in the complement of $A$, i.e. oputside of $A$, will have to be in the area in $B$ that is outside of $A$, and hence be in $B$, period. So: $A^C \subseteq B$
A: I suspect your confusion is that you need to know the ambient space to know what the complement of $A$ is. Suppose $A$ and $B$ both live in some bigger set $X$. The "complement of $A$" means $X\setminus A$, and the claim is that $X\setminus A\subset B$.
Pictorially, $B$ must cover all parts of $X$ which $A$ does not cover. The resulting picture won't really look like a Venn diagram per se, but you could, for example, draw the set $X\setminus A$ as a circle inside of $B$.
