As said in the title I am a little confused on the idea of traits located on the sex chromosomes. The example we worked on in class was haemophilia, a recessive trait located on the X chromosome. Does this mean males only have one allele to choose from while females have two? Does this mean that only females have the ability to be heterozygous in sex linked traits?
There is a specific term for this called hemizygous / hemizygote - meaning that only one allele of the gene is present. Therefore males cannot be heterozygous for genes on the X or Y chromosome (not counting for gene duplication or other chromosome disorders) since they naturally carry only one copy of these chromosomes.
All of the other answers are basically correct, I just wanted to add that there are some genes which are present in both the X and Y chromosomes, in the pseudoautosomal regions. These genes are inherited in an autosomal manner (hence the name). A male has two copies of each, just as a female would, and can thus be homo- or heterozygous.
In XY sex determination systems the females carry two copies of the X chromosomes, thus can be homo- and heterozygous. Males however, carry one X chromosome, meaning that all loci are hemizygous (excluding those with homologs on the X). Under conditions of complete dosage compensation, often through up-regulation of X linked loci, they are effectively homozygous, as demonstrated here where expression levels of X-linked genes are at a ratio of near 1:1 with autosomally linked genes.
An interesting potential consequence is that males will exhibit more additive genetic variance in X-linked loci.
Because males only have one X chromosome, they can only have one copy of any gene found on the X chromosome, and therefore only have one allele. This means that in the case of a recessive disorder like hemophilia, should they happen to inherit a recessive allele from their mothers, they will have the recessive (disordered) phenotype because there is no other allele present to give them the dominant phenotype.
"Homozygous recessive" and "homozygous dominant" are perhaps a little misleading here because male individuals aren't homozygous at all, having only one copy of genes present only on the X-chromosome.
But yes, this means only women can be heterozygous for sex-linked traits. Men will have either the dominant or the recessive phenotype, and cannot be carriers.
It sounds like you pretty much have it. Hemophilia is recessive, meaning that a single function copy of the necessary clotting genes will be sufficient to function. So a female can inherit defective genes on one X chromosome and functional genes on the other and be perfectly fine. However, if a male inherits defective genes on one X chromosome he will have the disorder because he does not have another X chromosome to provide the functional genes to compensate.
I realize that you also said you are confused about traits located on sex chromosomes. They are essentially just like any other chromosome and carry genes just like other chromosomes. It just so happens that they also carry genes that are important in gender determination.