How to write equations for dissociation of ionic compounds in water?
Your ionic charges are not correct for iodine. Looking at your attempt.

As $\ce{Be}$ is in group 2, the ionic charge for beryllium ion is fine, but iodine is in group 17, so its ion is $\ce{I-}$.  When the ions dissociate, they become aqueous or (aq) as the state of matter.

Then the ionic charges need to balance, thus:

$$\ce{BeI2 (s) -&gt; Be^2+ (aq) + 2I- (aq)}$$

To balance the ionic charges in this example, you need 2 $\ce{I-}$ (iodine ions) to balance the $\ce{Be^{2+}}$ (beryllium ion).  

A similar example (and further explanations) are provided on the UC Davis ChemWiki page Unique Features of Aqueous Solutions (including an example of the dissolution of $\ce{MgCl2}$ - another compound with group 2 and 17 elements).

So,


determine the group, hence ionic charge of each dissociated ion
balance these charges
state that the dissociated ions are aqueous


Now, use the process to determine the dissociation of $\ce{LiI}$