If you cast alter self, you can give yourself natural weapons (to increase unarmed strikes to 1d6):
You assume a different form. When you cast the spell, choose one of the following options, the effects of which last for the duration of the spell. While the spell lasts, you can end one option as an action to gain the benefits of a different one.
Natural Weapons. You grow claws, fangs, spines, horns, or a different natural weapon of your choice. Your unarmed strikes deal 1d6 bludgeoning, piercing, or slashing damage, as appropriate to the natural weapon you chose, and you are proficient with your unarmed strikes. Finally, the natural weapon is magic and you have a +1 bonus to the attack and damage rolls you make using it.
Would the caster be able to make an attack with them on the same turn, or would casting the spell take up that action?
I'm guessing it's the latter, but I just want to be extra sure.