How can you tell the difference between sp3, sp2, and sp hybridization?

At its core, the meaning of ##sp^n## is that one ##s## orbital mixes with ##n## number of ##p## orbitals close in energy to form degenerate (same-energy) hybridized atomic orbitals that can allow access to more electrons than available from “pure” (##s##, ##p##, etc) atomic orbitals for .

##sp^3## bonding involves using four ##sp^3##-hybridized atomic orbitals, so it must have four electron groups. EX: ##”CH”_4##

##sp^2## bonding involves using three ##sp^2##-hybridized atomic orbitals, so it must have three electron groups. EX: ##”BH”_3##, ##”H”_2″C”=”CH”_2##

##sp## bonding involves using two ##sp##-hybridized atomic orbitals, so it must have two electron groups. EX: ##”H”-“C”-=”C”-“H”##, ##:”C”-=”O”:##

I’ve explained ##sp^3## and ##sp^2## hybridization below, and from that, I think you can imply what ##sp## hybridization is.
##mathbf(sp^2)##-HYBRIDIZED BONDING
For instance, ##”H”_2″C”=”CH”_2## involves two ##sigma## bonds (one for each single bond), and then one ##sigma## and one ##pi## bond (used in one double bond), so three electron groups are needed, but 4 electrons need to be donated by carbon.
Since carbon has 4 , but its ##p## orbitals (which are highest in energy) only contain 2, it needs to mix two of the three ##2p## orbitals with the ##2s## orbital to make use of 2 more . This is favorable because it involves the lowering of the energies for two of the ##2p## orbitals, increasing stability.
This results in the usage of three ##sp^2## hybrid orbitals to bond: the ones with one electron for ##sigma## bonding to hydrogen, and the one with two electrons for incorporating one ##sigma## and one ##pi## bond with the other carbon.
1 ##2s## orbital had been incorporated, and 2 ##2p## orbitals had been incorporated, so it is called ##sp^2##, having ##33%## ##s## character and ##66%## ##p## character.
##mathbf(sp^3)##-HYBRIDIZED BONDING
A similar reasoning follows for ##sp^3## bonding. Let’s take ##”CH”_4## as an example. It needs four electron groups, and it needs to make four IDENTICAL ##sigma## bonds (one for each single bond).
4 are needed from carbon, but only 1 electron needs to be contributed per ##sigma## bond. So, we need four separate degenerate hybrid orbitals to make each ##sigma## bond. Therefore, all three ##2p## orbitals must mix with the ##2s## orbital and stabilize in energy overall to get four degenerate hybrid orbitals.
This results in the usage of four ##sp^3## hybrid orbitals to bond: the ones with one electron allow ##sigma## bonding to hydrogen.
1 ##2s## orbital had been incorporated, and 3 ##2p## orbitals had been incorporated, so it is called ##sp^3##, having ##25%## ##s## character and ##75%## ##p## character.
I think from here, you can imply what ##sp## hybridization means. (Hint: It can also be called ##sp^1## hybridization.)