How do ionic compounds dissolve?

Hint: Ionic compounds as the name suggests are composed of elements bound together by electrostatic forces of attraction which are among some of the strongest forces of interaction in a compound.
Dissolving a compound involves breaking up of bonds found between two species and then stabilizing these fragmented species by some process or method.

Complete step-by-step answer:When any compound is introduced in a solvent, the fact that whether it would dissolve or not dissolve depend on whether this compound and the solvent are alike in nature or not, in case of an ionic compound a solvent with charged species stabilizing capability would dissolve it for example water and a solvent with no such ability won’t be able to dissolve it. So factors like Hydrogen Bonding and other such interactions could easily stabilize the ions formed when an ionic compound is dissolved. The ions formed are cationic and anionic in nature thus both these species must be stabilized for the whole ionic compound to dissolve. Higher the dielectric constant more is the ionic compound dissolved in it.
Cations are electron deficient in nature and so the stabilizing factor would involve providing electron density via artificial or external means. Similarly, for anions which are electron rich species in nature we need stabilizing factors that attract electron density towards themselves thereby stabilizing the anions.

Note: We should be careful about what solvent is provided because depending on the solvent the ionic compounds may or may not dissolve and even if they do dissolve their extent of dissolution is completely different and proportional to the nature of solvent.