Unlike the 1000s of Starcraft pages out there, I'll assume that you've played Protoss before and know the units. I won't have any pictures or information on the costs of units and buildings here. If you're unfamiliar with Protoss units, then I suggest that you take a brief look at your Starcraft manuel.

Probe - You'll need lots of these guys since they are your workers. Keep in mind that a probe doesn't build a building. It'll just make it so that a building can warp at the location you designated. So you can send a probe to the location when you want a building and once he casts the warp portal, you can send him off to do something else (gathering resources, scouting, making more buildings, etc.)

Zealot - These are the protoss's first line of defense. Unlike the other two races, these guys are stronger but more expensive. Also, they are kinda slow. Despite all this, you should still build these guys anyways. Zealots rock in the beginning but they become less valuable as the game progresses unless you upgrade its speed in the Citadel of Adun. They can be really useful in taking out enemy siege tanks with this upgrade.

Strong Against : Siege tanks and marines.
Weak Against : Air units, firebats, more advanced ground units.

Dragoon - Once you're able to build Dragoons, don't build too many Zealots. Dragoons can hit just about anything visible within their range. These guys should be your main ground attack force early and mid game. Be sure you combine them with Zealots or their slow attack speed will be a great limiting factor.

Strong Against : Mutalisks, zerglings, and wraiths.
Weak Against : Siege tanks, firebats and battlecruisers.

Templer - These are the Protoss's spell-casters. They are rather weak, but you can still desperately save them when taken off guard. Have two of them pair together and turn into an Archon which is very strong.

Shuttle - These are the Protoss's means of transport via air.

Reaver - Reavers can do 100+ damage in one shot. They are powerful but not versatile since they cannot attack air units. However, they are good for defense, surprise attacks, or diverse armies.

Strong Against : Zerglings, marines, hydralisks, firebats, etc.
Weak Against : Siege tanks and air units.

Observer - You'll need these guys to see cloaked units. Seeing or not seeing cloaked units can make a HUGE difference.

Scout - These guys are fairly fast and strong. Have one or two of these guys patrol the outskirts of your base and combine these guys with the rest of your attack force for full effect.

Strong Against : Mutalisks, wraiths, and many ground units.
Weak Against : Missile turrets, photon cannons, spore colonies, battle cruisers, ghosts (lockdown).

Carrier - Carriers are probably the most controversial units in Starcraft. They are also quite unique. Carriers cannot deal any damage!! They must deal damage with the Interceptors they build and send off. You're in trouble if all of these Interceptors are destroyed in a Carriers-only army. These Interceptors only do 5 damage each (8 when fully upgraded.) Also, one Carrier can only hold 4 Interceptors (8 when fully upgraded.) Even when fully upgraded, a Carrier can only indirectly do 64 damage each "pass". And they cost a lot (like 800+ net resources including the Interceptors.) Multiple units with a total net cost less than this can destroy one Carrier (like 4 Hydralisks.) Despite it's resource inefficiency, these guys can do a fair job if you integrate them into your army and air-force. Also, they are pretty good for a hit-and-run attack. Just attack some workers and have the Carrier retreat while the Interceptors continue to do damage. They also have a great range too. The interceptors can travel great distances and you can destroy a missile turret by sending Interceptors and gradually replacing them. If nothing attacks your carrier, it can destroy the missile turret without taking any damage. Good luck when using these guys. They can have a lot of potential when used EXACTLY correct. I consider these guys as the Protoss's "wild-card".

Strong Against : Missile turrets, mutalisks, wraiths, bunkers, ground units without without surface to air attack.
Weak Against : Battle cruisers (yamato gun), ghosts (lockdown), scrouges.

Arbiter - I never really learned how to use these units except to make my other close-by units invisible to most enemy units. These guys themselves don't become cloaked, so you should watch out if someone tries to target them when you're attacking with an invisible army that depends on these guys to be cloaked.

Archon - These are pretty powerful and fairly versatile units. Unfortunately, you have to sacrifice 2 templers to make one of these. Think twice before doing so, but once you do it, you probably won't regret. This is another wildcard in this race.

Strong Against : Mutalisks, ultralisks, wraiths, guardians and zerglings.
Weak Against : Siege tanks, battle cruisers, science vehicles (EMP Shockwave).