Hold the 'Alt' key and hover over the target to see your attack odds and a breakdown of the bonuses the defender has.
Barbs only spawn in the fog, so Fogbusting is a good skill to develop. On lower levels the AI can take a while to fill in the space, so barbs are trouble a little longer than at the higher levels.
I generally just send out a mass warriors to fogbust. You don't need to eliminate all the fog, just have a unit within 2 tiles of a fogged square and a barb won't spawn there.
Something like:
OOOOO
OOOOO
OOXOO
OOOOO
OOOOO
Where 'X' is your warrior or any unit. The outer ring of tiles may be fogged, but a barb will not spawn there becuase it is too close to your existing unit.
Put two side by side and you will by blocking 50 squares from barb spawn:
OOOOOOOOOO
OOOOOOOOOO
OOXOOOOXOO
OOOOOOOOOO
OOOOOOOOOO
This will work for barb galleys too, so get some warriors near the coast too and stop them before they start spawning.
Before you have your net of units out blocking barbs from spawning fortify your units on a forested hill +75% defense, forest +50% defense, or hill +25% tile. I almost always park them in forest. If they are there a few turns the fortify bonus will add up to another +25%. I also take the Woodsman promotions (W1 +20 forest/jungle defense, W2 +30 forest/jungle defense) for these early fogbusters to further help their defense.
Later when more advanced unit spawn (late warriors, archers, axe/spear) they will ignore some parked fogbusters and head for an improvement (roads included) or a city (whichever is closer to them). So try to determine their target and fortify a unit on your improved tiles. An archer on a hill can hold things for a little while longer until your spawn blocking is 100%.
Edit: Defense %forest