Google: galciv2 wiki

There's a good wrirte up there with charts under "shields".

Basically, you have to research:

1) Galactic Warfare, then

2) Space Militarization, then

3) Starship Defenses, then

4) Shield Defense Theory

That gets you Deflectors (first level) with a defense value of one each.  Each next level reduces size. 

Then you get Shields (first level) with a defense value of two each.   Each next level reduces size,

Etc.

(One addendum - some races start with Galactic Warfare and/or Space Militarization.  If your race is one of those, or have "bought" that tech in the game race set-up, then you just pick up the Research at the next step.)