You are a scientist who discovers three new species of beetles in the jungles of south america. describe, in detail, how a protein found in each of these beetles can be used to determine which species are more closely related

Sunset, this is really similar to the question about molecular clocks you asked. The more closely related the three species are, the more similar the homologous proteins will be in each of the species.
 

Defining 'sequence similarity' is a little bit nuanced. It can refer either to the genetic code or the amino acid code. Because the genetic code is degenerate multiple codons code for the same amino acid - mutations in the gene don't result in mutations in the proteins when the mutated codon codes for the same amino acid as the unmutated codon.
 
Similarly, you can sort of think of some amino acids as being redundant. In some cases, replacement of one amino acid with another doesn't result in all that much change to the protein's structure or function. The result is, as species diverge and mutations build up, they build up preferentially in certain domains of the protein and more frequently involve replacement of one amino acid with one which is pretty much similar to it.

Since all of the three beetle species posses the protein, we can use it to determine their relations. The more differences there are in amino acid sequences and the structure of the protein, the species are more distantly related because they have diverged a long time ago.