3 Check Opening Ideas For Black In the French Sicilian: Part 1 (5. exd6)

Plans and ideas:
 

Play for activity and the initiative.
Don't focus on material. You will often be down a Rook or more in this line.
You can sometimes allow your opponent to get 1 or even 2 checks in exchange for active pieces and/or a strong counter attack.
Look for opportunities to play Nd4 to threaten checks on f3/e2/c2 and/or to deflect White's Knight away from defending the Kingside. You can often even play Nd4 when White has Bxd7+ in response.
Look for opportunities to sacrifice your Queen when White castles Kingside.
Use your Kingside pawns to attack White's castled King if needed.

Where to put your pieces?

The Queenside Knight goes to c6 and later d4 if possible.
The Queen recaptures on d6 and then goes to c7, d5 or b8 after it is attacked depending on where White's pieces are.
The light squared Bishop goes to d7 and later can go to c6 or e8 to open the d-file. 
The King usually castles Queenside but if that is not possible then castle Kingside. You can even leave your King in the center in some lines.
The Queenside Rook is sometimes captured by White's Knight but if it isn't then you can try to lift this Rook to d5 where it has potential to swing over to the Kingside.
The Kingside Knight usually goes to f6.
The dark squared Bishop goes to d6 in most cases. e7 and c5 are also possible.
The Kingside Rook can stay on the h-file to support the h-pawn advance. If your Knight is captured on f6 then put your Rook on the open g-file.