The most common examples are either insertion or deletion.
Insertion mutations occur when an extra base pair is inserted into the DNA sequence. If this insertion is in a gene coding region of the DNA, any RNA transcripts will contain the same insertion and the polypeptide chain will have a different order of amino acids which will change the shape of the protein.
Deletion works the same way except instead of an insertion of an extra base pair into the DNA there is a missing base pair. This will also alter the RNA, Polypeptide and functioning protein.