How does adding acids (H+ ions) to limited soluble salts help it further dissolve?
In general, the solubility of a sparingly soluble salt having a basic anion will increase with the addition of a strong acid.  Given:  

$$\ce{X+A- &lt;--&gt; X+ + A-}$$  

where $K_{sp}$ is small and A- is a weak base, the addition of a strong acid will form HA, driving the reaction to the right and increasing $K_{sp}$.  

In the specific case of  

$$\ce{CaF2 &lt;--&gt; Ca^2+ + 2F−}$$  

the addition of $\ce{HCl}$ gives  

$$\ce{CaF2 + 2HCl &lt;--&gt; Ca^2+ + 2Cl- +2HF}$$  

driving the reaction to the right, thus increasing the solubility of $\ce{CaF2}$.  Note that $\ce{HF}$ itself is a weak acid, having a pKa of $3.17$, and will be in equilibrium with $\ce{H+}$ and $\ce{F-}$.