Let $A$ be a finite dimensional basic and connected $k$-algebra for $k$ an algebraically closed field. There is an isomorphism: $$ H^n(A) \cong Ext_{A^e}^n(A,A) $$ which is given by noticing that the bar resolution is a projective $A^e$-resolution of $A$.
The direct sum of the cohomology vector spaces has an algebra structure given by the cup product, and the direct sum of the Ext's is also an algebra with the Yoneda product.
How do we prove that they are isomorphic as $k$-algebras?
For an exact sequence $\epsilon \in Ext_{A^e}^n(A,A)$, lift the identity map of $A$ to the bar resolution via the comparision theorem, since the bar resolution is an $A^e$-projective resolution of $A$. The last non-zero (from right to left) vertical map of this lift is a morphism from $A^{\otimes(n+2)}$ to $A$. Then send $\epsilon$ to the Hochschild cohomology class of this last non-zero map. It is well defined because the comparison theorem says this map is unique up to homotopy.
The only thing left to prove is that this map is a morphism and that it sends the Yoneda product to the cup product. Wich is straight-forward.