Genetics are confusing. So I will explain what I understand, but even that is somewhat limited.

 

Phenotype: what they physically look like

Genotype: Their genetic makeup “code”

Heterozygous: Different genetic codes eg: D/d 

Homozygous: Same genetic codes eg: d/d

 

A wildtype is dominant D (dark), and will always be heterozygous  =    D/d

 

A leucistic is recessive to wildtype but dominant to albino. It will always be homozygous =    d/d

 

An albino is recessive, and homozygous = a/a

 

A golden albino is always either D/D a/a or D/d a/a. The albino gene is always recessive homozygous a/a, and the dark pigments which help make the axolotl gold are written as D/D or D/d.

 

An axolotl's parentage is very important in breeding. If they come from different parents, it can greatly affect the outcome of their offspring. A leucistic, although d/d, may have an albino parent, so is recessive for albino, and with the right pair up, can create albino babies, despite not being an albino itself. Another axolotl who was albino, or recessive for albinism would be needed.

 

Dominant genes, such as the dark pigment in wildtypes and golds, need only one to show up in offspring, whereas recessive genes, such as leucism and albinism need one from each parent to show up. 

The dark gene will generally counter leucism, and albinism (turns out golds instead of whites), but it depends on the two genotypes being combined, and punnet squares are (somewhat) useful for this, on the most basic level.