how can mutations change the gene pool of a population?

Answer 1

Mutations very rarely change the gene pool. All mutations result in reduced genetic information (or at best are information neutral). Most are harmful and the tend to be selected out by natural selection.
Occasionlly they can be beneficial - for example sickle cell anaemia is caused by an inherited defect in the instructions which code for the production of haemoglobin. The defect has the benefit of making the sufferer immune to malaria.
Strangely, this is sometimes touted as an example of upwards evolution!
http://www.creationontheweb.com/content/view/901

Contrary to the above - mutations do not create alleles.
All (sexually reproducing) organisms contain their genetic information in paired form. Each offspring inherits half its genetic information from its mother, and half from its father. So there are two genes at a given position (locus, plural loci) coding for a particular characteristic. An organism can be heterozygous at a given locus, meaning it carries different forms (alleles) of this gene. For example, one allele can code for blue eyes, while the other one can code for brown eyes; or one can code for the A blood type and the other for the B type. Sometimes two alleles have a combined effect, while at other times only one allele (called dominant) has any effect on the organism, while the other does not (recessive). With humans, both the mother’s and father’s halves have 100,000 genes, the information equivalent to a thousand 500-page books
http://www.creationontheweb.com/content/view/3831/

Answer 2

The gene pool contains all the different alleles for that population. A mutation can produce a new kind of allele that wasn't there before. So a mutation can change the gene pool.

Note: if the the mutation is fatal, then it doesn't change the gene pool because the individual doesn't survive to pass it on.

Answer 3

Through procreation.