The carbon atom has ##sp## hybridization; the ##O## atoms have ##sp^2## hybridization.
You must first draw the Lewis structure for ##CO_2##.
According to theory we can use the steric number ##(SN)## to determine the hybridization about an atom.
##SN## = number of lone pairs + number of atoms directly attached to the atom.
We see that the ##C## atom has ##SN = 2##. It has no lone pairs but it is attached to two other atoms. It is ##sp## hybridized.
Each ##O## atom has ##SN = 3##. It has 2 lone pairs and is attached to 1 ##C## atom.
Just as the carbon atom hybridized to form the best bonds so do the oxygen atoms.
The valence electron configuration of ##O## is ##[He] 2s^2 2p^4##.
To accommodate the two lone pairs and the bonding pair it will also form three equivalent ##sp^2## hybrid orbitals.
Two of the ##sp^2## orbitals contain lone pairs while the remaining ##sp^2## orbital and the unhybridized ##p## orbital have one electron each.
We can see this arrangement in the ##C=O## bond of formaldehyde which is equivalent to the right hand side of the ##O=C=O## molecule.
(from www.slideshare.net)
There is a similar arrangement on the left side of the ##O=C=O## molecule but the ##pi## bond is horizontal rather than vertical.
Here is a video on the hybridization of carbon dioxide.