Assuming no changes between original and Born of Blood expansion.

Shields encompass the entire ship, absorb incoming fire, and shut down after too much damage to reboot.

Deflectors are a forward facing hemisphere that block projectile and missile weaponry, letting energy weapons pass through.  They do not drop after too much damage.  Massively powerful against forward facing weaponry, particularly missile loaded enemies relying on range to win.  Completely pointless when the enemy isn't in that frontal area and shoots around the bubble.

Shields are extremely useful in just about any situation.  With an advanced command section, shielded destroyers still have excellent firepower and actually survive engagements against cruisers, dreadnaughts generally wipe them out instantly anyway.  Deflectors are more of a key role thing.  Against a high defense planet, that stream of missiles coming at you can be rather devestating.  You can drop very powerful planets with relatively weak forces if they have deflectors up because the defense just doesn't matter against them.  The planet can't circle around behind them, and doesn't get to use anything but planetary missiles.

As far as humans go, both shields and deflectors are a random tech.  You're never guaranteed to get either of them.

Shields and deflectors aren't a necessity.  They're nice to have, but it's a trade off on something else.  The alternative modules have significant advantages in firepower, so you give up that durability increase in return for significantly higher damage output.

Mark 4 shields take 2500 points of damage and have a 10 second recharge.  They are very expensive as well.  The shield command section on a cruiser only has four small mounts, the battle bridge command section has two medium mounts, one large mount, and one special beam weapon mount.  The cutting beam, a high level beam weapon for use in the special beam weapon mount, does 1800 damage over 3 seconds, 700 points left on that shield.  It's very easy to drop a shield section and still out damage the hull with a battle bridge instead.

You have a 40% chance of getting deflectors on game start, a 50% chance of getting shields after researching deflectors, and a 40% chance of getting shields after researching fusion.  You then have a shot at later shields off of other technologies, like antimatter.  If you don't get any shields at all the entire game, you've still got plenty of other things to use.

Edit: This site is your friend.  Much information there, including all the different research odds.

Yeah, it definitely doesn't follow that model.  I'm getting my ass kicked right now because my shielded destroyers suck.  They're bloody wonderful when you have twice the fleet size, but they really get reamed against just as many destroyers with the 4 weapon deficit if the enemy has a shield disrupting weapon.  Some of the high level shields are utterly badass, but for SOTS, they seem to be more of an important unit addition than a good idea in general.  It's always a good idea to shield your command units for instance.