How does a trait become associated with genetic loci?
It is possible for a previously negligible trait to become heritable.
For example, some phenotypes are under sexual selection, but clearly were not always under sexual selection (such as the Peacock's plumage).
How do traits like this become heritable?
If a parent favors offspring with traits that the parent shares, would this cause these traits to become heritable?
The whole question is based on the assumption that it makes sense to talk about genetic trait, while it is actually a little bit undefined. The closest existing concept you might want to read about is the concept of heritability. Please see my comments in your text and especially the links on heritability.
Evolutionary psychology and genetics how does a trait become genetic
I don't understand why you are talking about evolutionary psychology in your title. The rest of the post seems unrelated.
As you have received a downvote which might be related to your title, I have now edited your title.
How does a trait become genetic?
It is unclear by what you mean here. But you should probably read about the post Why is a heritability coefficient not an index of how “genetic” something is?.
If a trait is passed down from parent to offspring how is it made that the trait is passed along as heritable.
Again, this is unclear. From the above link post, if at least part of the variation for a phenotypic trait is caused by genetic variation, then the trait is heritable (heritability differs from zero). If a trait is heritable, then parents and offspring will tend to look alike (see Why does the slope of parent-offspring regression equal the heritability in the narrow sense?).
If a woman is similar to her mother and she is sexually selected on this basis. Would this make the trait become genetic?
I don't understand why you are talking about sexual selection here.
Note that selection act on population, selecting specific genetic variants. Talking about an individual being selected just mean that the individual is carrying the genetic variant that is associated with higher fitness in the population.
Note also, that without heritability, there is no selection. You should have a look at Lewontin recipe, for example at the post How does Darwinian Evolution work?.
Parent favors Offspring with traits that they have that are similar to their own selves.
Do they? In humans? In other species? It would require a reference to really what process you are referring to and whether it is actually true.
Would this make it genetic?
Again, this is unclear unfortunately.
