What is the effect of adding HCl on a certain solution at equilibrium? If we have 
  $$\ce{CH3COOH + H2O &lt;=&gt; CH3COO- + H+}$$
   what is the effect on acetate ions when adding each HCl and NaOH to the solution?  (State why according to Le Chatelier's principle) 


Le Chatelier's principle states that if any of conditions of a chemical reaction at equilibrium changes, the reaction will shift to a direction to oppose that change and restore the equilibrium.

I guess adding $\ce{HCl}$ will increase hydronium ion concentration so the reaction will be shifted to the left side, accordingly acetate ions concentration will decrease. If we add $\ce{NaOH}$, this will increase water concentration so the reaction will be shifred to the right side accordingly increasing the concentration of acetate ions.
You are absolutely correct. Adding $\ce{HCl}$ adds protons to the mix, which you can imagine as applying pressure on the right-hand side, which means that the reaction will shift backwards slightly and the acetate concentration will decrease. For $\ce{NaOH}$, you also need to consider the underlying equation:

$$\ce{H2O &lt;=&gt; H+ + OH-}$$

which will be shifted to the left by additional hydroxides. This means that the overall proton concentration decreases and you can imagine that as lifting a weight from the right-hand side: The reaction will shift forwards.