I've been playing the first Starcraft and playing games against the AI.
 
Against the Terrans I ran into the same problem over and over again. Those god damn cloaked Wraith planes. Missile turrets can detect them, but what do I counter them with if I want to take a group of units and attack the enemy base?

Use either the comm center or a science vessel.

Take in a Science Vessel for the Terran, or use the comsat station scanner sweep to detect them, but that wears out over time. 
 
Each race has a detector that you should bring into combat if you expect to run into cloaked units. In Starcraft 1, those units are Overlords for Zerg, Science Vessels for Terran, and Observers for Protoss. 
 
SC2 has a very similar system, however the units are different (some of them are).

Also to clarify, I'm playing as the Terrans myself. 
 
Figured that would make the most sense to me as a new player, considering I'm going to play the campaign first anyway, and SC2 only has the Terran campaign.
 
So I'd try them out while playing 1, and be sort of used to them already when starting 2

Pardon the late reply. Like what was said above, just bring Science Vessels to detect them and either your own flying assault units or Marines for attacking. Make sure to protect them with the Science Vessels!