Under all "normal" circumstances, the great majority of anyone's genetic traits come from both parents.
Humans are diploid organisms, meaning that we have two copies of every chromosome, and therefore two copies of every genetic trait. We are produced by gametes (sperm and eggs) each of which are haploid (having only one copy of each chromosome). These single copies are contributed by each parent, basically by taking their own two copies, shuffling them, and then putting a single copy in each gamete. You could think of it like having two different recipes for cookies, shuffling the ingredients, then rewriting each new recipe in its own cookbook.
Notable exceptions come in the form of the sex chromosomes, X and Y. The Y chromosome is significantly smaller than the X chromosome, and is thought to have derived from a small portion of the X. Therefore men will exhibit certain traits more obviously than women because their single X chromosome does not have a competing allele, due to the region at which this competing allele should exist being absent on the Y chromosome.