Two Countries: US and Argentina
Two goods: Cattle(C) and Automobiles(A)

The US is more efficient in both producing cattle and Automobiles:

US
C: 10 hours
A: 30 hours

Argentina
C: 15 hours
A: 65 hours

One would think that, opening trade barriers, the US would pwn Argentina, but NOEZ. Why?
Because we just win at life. That, and comparative advantages.

Comparatively, Argentina is less efficient in the production of Automobiles: 65/15 = 4.3; it takes 4.3 times labor to produce a unit of Automobiles than to produce one unit of Cattle.
Whereas the US : 30/10 = 3

But if we take it the other way round, Argentina is more relatively more efficient in the production of Cattle: 15/65= 0.23, the US: 0.33.
So what Argentina should do is focus on cattle, and import cars from the US.

That's why the title to Comparative Advantages is "Uncommon sense". I lol'ed, but you might not, given that you're not a nerd.
AAAANYWAY.

Let's say Argentina has 10,000,000 units of labor, and the US 150,000,000. If they use half for each product, their production would be:

C= 333,333 (that is, 5,000,000/15)
A= 76923

And the US:
C= 7,500,000
A= 2,500,000

So, let's say Kirchner and Bush (or the Blacky) have a meeting, they say hello, how are you, how's the wife, and Great K says: "I have an idea! Let's eliminate all the tariff thingies and stuff!!111" , Buch says "mmmk"; Argentina focuses on what it does best, implode, I mean raising cattle, and the US focuses on what does best, killing innocents, I mean, manufacturing toyotas.

Let's suppose that given that the us is a nice country (big assumption), trade terms lye in between the country's prices, that is (4.3+3)/2 = 3.6

So Argentina now only makes cattle:

C= 666,666 (TEH DEVILZ)
A= 0

And we say: WE WANTZ CARZ, let's say 90,000. So according to our previous trade terms (Argentina respecting international agreements!! This example is a big fat lie) we buy these 900,000 cars with 324,000 units of cattle, so Argentinian consumption would be:

C= 342,666
A= 90,000

See? we now have MOARZ EVERYTHINGZ!!! =D we jumped from 333,333 unit of cattle to 342,666, and from 76,923 cars to 90,000. Now you're probably thinking: "OH NOEZ THE MEXICANS SCROOD US!!1!!"
Well, no, let's see how the US looks like:

Let's say you were only interested in moar cattle, so, in order to make your car production stay the same, you had to increase it by 90,000, that made you stop making 270,000 units of cattle. So you now produce:

C= 7,230,000
A= 2,590,000

but you gave 90,000 cars to receive 324,000 units of cattle, so you actually consume:
C= 7,554,000
A= 2,500,000

So yay! you've been benefited as well!, you now have 54,000 more units of cattle now! But, as you might have seen, we benefited more: why? I told you we simply win at life.And a little detail that smaller countries always benefit more ^_^

But we need to measure the benefit, so let's consider this:

Argentina: Before trade a worker had to work 80 hours (65+15) to buy a car and a cute cow.
Now, with the wonders of trade, a worker still has to work 15 hours for a unit of cattle, since they are manufactured in the country but now only
15x3.6 (trade term) = 54 hours, for a kewl Honda, adding up 69 hours.
So Bt (Before trade)= 80
At= 69
(69-80)/80 = 13,75% rise in real wages.

US:
Bt: 30+10 = 40
After trade, we'll have to consider that not ALL of the cattle you consumed was Argentinian, so only a part will be consumed at the foreign trade price (10/3.6= 8.33)
(7,230,000x10+324,000x8.33)/(7,554,000 9)
That complicated math thingy equals 9,92
So after trade the US workers real wage is:

30+9.92= 39.92, 0.2% rise

Ha! I told you we had benefited more. Our foreign relations Ministry not only did not screw ourselves up, but also tricked another nation!!! This is just too much fantasy.

Actually, it is. All I have said are lies.
But I'll leave that for another blag.