Question

How the proteins are classified?

Answer 1

In too many ways to list!

Some of the main classifications are by their structures:

Primary: the amino acid sequence (peptide bonds)
Secondary: the local structure due to the local amino acid sequence (hydrogen bonding interactions)
Tertiary: the structure of the peptide due to folding between different peptide side chains (other noncovalent interactions)
Quaternary: the structure of the protein due to the interactions between more than one peptide

Some classifications involve the quaternary structures:

Fibrous: long filamentous structural proteins such as `alpha`-keratin, and collagen
Globular: spherical complexes of thermodynamically favored folding that maximize hydrophobic packing and minimize caged water interactions such as hemoglobin and immunoglobulin

Others involve the amino acids:

Nonpolar, aliphatic: Pro, Ile, Leu, Ala, Glu, Val, Met
Nonpolar, aromatic: Tyr, Trp, Phe
Polar: Cys, Ser, Thr, Asn, Gln
Basic (positively charged at physiological pH): Lys, Arg, His
Acidic (negatively charged at physiological pH): Glu, Asp

I could go on, but this should suffice.