Kassadin has multiple item paths; he can go caster via Mana and Ability Power or anti-caster with Cooldown Reduction and Magic Resist.
Kassadin's ultimate has many uses and is on a shorter cooldown than most, use it often.
Try to get the Ancient Golem buff to counteract Riftwalk's increasing Mana cost.
Kassadin deals mostly magic damage. If he's doing well consider buying magic resist items like Mercury's Treads and Banshee's Veil.
Each time Kassadin consecutively uses Riftwalk, he pays more and more mana. Keep this in mind as you chase him.
It takes 6 spell casts for Kassadin's slow, Force Pulse, to become castable. If he levels up that ability, judiciously use your own skills while laning against him.