TL;DR Version
To sum up the points below:
- Westeros is roughly equal to size of South America in our world as per the author.
- Essos is equal to Europe and Asia combined according to the author.
- And no, GRRM doesn't want you to be sure how long will it take to travel from point A to B. But he has given a pointer to roughly estimate the size if you really want to. That is the length of the wall.
Longer Version
How do ASOIAF regions compare to our world?
George R.R. Martin has compared Westeros to South America and Essos to Eurasia . He said:
I will post the dates and times of my signing tour in the "touring"
thread uptopic. Thanks for asking.
As for your other questions (boy, you folks are relentless), I don't
have the precise population of King's Landing on[sic] the exact area of
Westeros immediately on hand.
In very general terms, however... King's Landing is more populous than
medieval London or Paris, but not so populous as medieval
Constantinople or ancient Rome.
Some readers have likened Westeros to England because they see some
general similarities in its shape, and in its location off the west
coast of a larger landmass. The latter is true enough (I don't see the
former, myself), but Westeros is much much MUCH bigger than Britain.
More the size (though not the shape, obviosuly) of South America, I'd
say.
The other continent is bigger (Essos), Eurasia size.
Yes, a league is three miles.
Should you worry about how long it takes to travel in Westeros and how big it is?
Also George R.R. Martin is deliberately vague about such matters. He said in another correspondence with the fans:
I have deliberately tried to be vague about such things, so I don't have obsessive fans with rulers measuring distances on the map and
telling me Ned couldn't get from X to Y in the time I say he did.
However, if you really must know, you can figure out the distances
for yourself. The Wall is a hundred leagues long. A league is three
miles. Go from there.
But if you turn up any mistakes in travel times by using that measure,
let it be your secret.
You really wanna know, don't you?
If, to quote GRRM, you are really that obsessed fan, Well put that calculator and ruler back. Another fan has roughly done the work for you by estimating the size. According to his/her findings:
Total length of Westeros from the North Pole to the coast of Dorne: 5084.06 miles
Distance from the Wall to the North Pole: 2,086.46 miles
Distance from the Wall to the treeline in Thenn: 595.7 miles
Distance from the Wall to the Arctic Circle: 300 miles
North-South Distance of the Seven Kingdoms: 2,997.6 miles
North-South Distance of the Lands Beyond the Wall (to the edge of the WoIaF map): 1,865.2 miles
Combined North-South Distance of Mapped Westeros: 4,862.8 miles

Disclaimer: These findings are not the official position of the author or the publishers. Any error's responsibility lies with the original poster. To clarify the confusion some members may have, The creator has based his recordings on a common reference system which he established from the Data GRRM has provided, explains his research in detail and identifies the potential issues with his work. I suggest taking a look at his blog post linked above..