How might a single base substitution in the sequence of a gene affect the amino acid sequence of a protein encoded by the gene, and why?

The effect differs. It could produce a different amino acid in the sequence because the corresponding codon has changed. It could also prevent the production of the originally intended sequence by changing one of the amino acids of a "start" codon (aka AUG) or extend the protein's sequence by modifying a "stop" codon (UAA, UAG, UGA or UGG), producing a new protein that might be useless or have different effects on the cell.