You can't research them [corvettes] until mission 4 (Earth campaign, anyway).
I think it's then mission 5 when you can build them in your bases [planets/moons/actual base?]
It says any research in a given mission is carried over to the next and the tech given there.
Edit : You've also researched the weapons it told you to? The Turrets, the blasters and the other one? They're researched fairly quickly, so you should do those, too.
Ok, in Mission 4 (Earth) when you research the corvettes, you select the moon Io, that's your base, and click the far left-middle circle button (ship) and it'll turn blue. Then click the top rectangular button below the middle of the screen (there's 4 or 5 in a column) and on the popup menu select "Corvette (B)" for a group of 4 Blaster Corvettes to be built around Io, or "Corvette (T)" for a group of 4 Turret Corvettes to be built around Io.
You can have 5 groups of ships, total (including the 3 or 4 fighters you probably brought in from the previous mission). Once a fighter group is shot down by the enemy's corvettes, you can replace them at Io with your own corvettes.
