Hybridization is part of the Valence Bond Theory (!= Molecular Orbital Theory). It is used to explain the geometry of a molecule.
First, draw the Lewis structures of both the nitronium ion (NO2+) and the nitrite ion (NO2-):
NO2+ forms two bonds (double/triple bonds count only once). Therefore, hybridize the s and one p orbital. The molecule has four outer electrons, so two go into the hybridized orbitals to form sigma-bonds. Pluck the other two into the remaining two p orbitals, which will form pi-bonds. Two hybridized orbitals means sp1 = linear molecule.
NO2- also forms two bonds. However, it has six outer electrons (two build a lone pair), and therefore, we hybridize the s and two p orbitals. Ergo, you get sp2 = a trigonal-planar shape.