HOLD ON. You can explore? Look for Earth?
Yes, but it's pretty tough and it will take a while, though.
You have to follow the story from the show ( almost literally, to get the Arrow of Apollo for instance, you have to do some weird but "canon" stuff ).
You can also go to New Caprica, which is also the only mission the plays in a atmosphere.
Kobol is also there ( the City of God's is a bit ...weird... ).
They have a working FTL, so you can jump around ( using the console, you enter coordinates directly...).
It isn't only a neat feature to save the time flying from one location to another, it can save your life ( the random AI ships are tough Bastards ) and a lot of money ( if you have the cargo hold full of goods and your ship is destroyed you loose everything! ).
Don't even thing of starting a "mission" on your own. You'll loose.
Those Missions are made for multiple players, you manage to destroy the first wave, the second one will mopp you up, even if you have the best fighter under your a**.
You can buy Battlestars or Basestars, but you have to fly A LOT of goods from one place to another.
You start with shuttle and a few bucks.
The fighters lack the FTL drive and have small cargo capacity, but you can handle yourself vs threats.
The bigger ships ( Colonial One, other Freighters have a HUGE cargo hold, but you're screwed if the AI or players attack you, even the ( up to ) 10 turrets on Colonial One wont save you.
All in all fun to play, but it takes forever to get a better ship.