Why are the shields not upgraded

Some subsystems have a small "head" icon above their power levels. These systems are:

• Piloting
• Shields
• Weapons
• Engines

By staffing these systems with a crew member, you increase the abilities of that system. When you send a crew member into an unstaffed room, you can see them head straight for the console and start working there.

From my observations:

• Staffing the Cockpit and the Engine Room increases your chance to dodge.
• The Engine Room also has the added benefit of reducing FTL charge time when staffed.
  • Please note that staffing the Cockpit is required for almost everything; the engines won't recharge even if someone is manning the Engine Room. Your dodge chance also goes to 0% if no one is trying to pilot the ship; it's an inert hunk of metal.
• Staffing the Shield System results in shields recharging faster.
• Staffing the Weapons System results in your weapons charging faster.
• Staffing the Door Control System results in your doors upgrading a level.
• Staffing the Sensor Control System results in your sensors also upgrading a level.

The amount of the benefit you receive is based on the crew member's system skill level, which you can see by going to Ship --> Crew, and hovering over the crew member. They will gain experience by working on the system, increasing the bonus they provide to the relevant system. You can occasionally see your crew gain experience by seeing yellow icons appear above them. These icons will match the system they are currently working on.

Note that it doesn't seem like crew gain experience when the ship is not in danger, so staying in a system doing nothing is unlikely to help your crew gain experience.
The exception to this, as @Halfwarr noted, is asteroid fields. Since your ship is continually in danger and the asteroid damage can be mitigated, this is probably an excellent way to gain skill. This is no longer valid with the full release.

Also, there is only a single console per system, no multiple crew members do not provide any bonus beyond faster repair speed in the event the system becomes damaged. This is easily testable by sending another crew member to the cockpit; the first one will provide a bonus to dodging when he reaches the console. The second will not increase your ability to dodge.

I have not unlocked all ships, however, so it may be possible that some of the later ships have multiple consoles for some or all systems, in which case, multiple crew members would provide a greater bonus.

From this page:

Humans comprise the majority of both the Galactic Federation and the Rebel Fleet. Humans learn skills faster due to their reduced XP ability, have no notable weaknesses and are the cheapest race to hire from Stores.

• Skills improve slightly faster (10%)

Engi originate from the Engi Homeworld. They take 50 to hire, with the following special traits:

• Repair speed is doubled
• Combat damage is halved

The Mantis originate from the Mantis Homeworld. It takes 45 to hire them.

• Inflict 1.5x damage in combat
• 1.2x move speed
• Halved repair speed

Rockmen are strong creatures and take 65 to hire. Their abilites are:

• Immune to fire
• Movement speed is halved
• Health is increased to 150%

Zoltan usually appear in Engi Homeworlds or Engi-Controlled Worlds. They appear rarely, and it takes 65 to hire them. Their special abilities are:

• Provides (1) power to occupied system
• Health is 70
• Explode when killed, damaging all enemy crew in the room

Slugs are one of the rarest crew to find. Their advantage is the ability to see your enemy's crew, and to be able to see the rooms surrounding the slug in your ship if your sensor goes down. They cost 45 to hire.

• Telepathic powers reveal rooms and lifeforms even when sensors are down.

The Lanius are scavengers – metallic lifeforms that rely on the absorption of minerals to sustain themselves. They are available only in advanced edition and even then are almost exclusively found in the Abandoned Sector where they cost 50 to hire. They need no oxygen and also drain oxygen from the room they are in.

• Drains oxygen from rooms
• -20% movement speed
• No damage from suffocation

And a final 'secret' race:

Crystals can be found in Life support pods that are revived by scientists. Doing so also begins a special quest to the Rock Homeworlds.

- Lockdown power: When finished charging, sends crystals to surround the room they are in, making it completly invincible to damage (Only that specific room). Nothing can exit/enter the specific room until the ability wears off.
- Reduced suffocation damage
- Movement speed -20%
- Health 125