How many sigma and pi bonds do sp, sp2, sp3, sp3d, sp3d2 have?

Without knowing more context, it's not possible to know the number of #pi# bonds.

If you want to get the number of #pi# bonds, know what compound you're looking at, and just count them.

One pure double bond has one #sigma# and one #pi# bond, and one pure triple bond has one #sigma# and two #pi# bonds.

From knowing the hybridization of the central atom, we can determine the number of #sigma# bonds around the central atom, but no more than that without more information.

Examples:

• #sp# hybridization in acetylene corresponds with two #sigma# bonds around one carbon.
  

• #sp^2# hybridization in ethene corresponds with three #sigma# bonds around one carbon.
  

• #sp^3# hybridization in methane corresponds with four #sigma# bonds around one carbon.
  

• #sp^3d# hybridization in #"PF"_5# corresponds with five #sigma# bonds around one phosphorus.
  

• #sp^3d^2# hybridization in #"SF"_6# corresponds with six #sigma# bonds around one sulfur.
  

You can see that the number of orbitals used in the hybridization spits out the same number of hybridized orbitals that can #sigma# bond. That is, you get five #sp^3d# orbitals, for example.

Therefore, the number of orbitals used in the hybridization is the number of #\mathbf(sigma)# bonds made around the central atom.