I'll add to those disagreeing with Chris Perkins. Counterspell is a reaction. I see nothing in the rules that says you can't cast one if you also cast a spell as long as you still have your reaction available. Counterspell is somatic only so you'll need a free hand. If your original spell has no somatic components, you need one free hand. If it did have somatic components you'll need two hands - one for the original spell and one for counterspell.
The somatic component is, of course, flipping the bird. "The enemy wizard casts fireball" "HA! I counterspell him" "He flips you the bird. Roll a Dex save."
The somatic component is, of course, flipping the bird. "The enemy wizard casts fireball" "HA! I counterspell him" "He flips you the bird. Roll a Dex save."