How does a wolf become dominant?

Usually, this never happens. The Alpha wolf never mates with an omega because omegas are considered as the lowly wolves; they never get along. Unless you're talking about the movie, of course :)

True, an alpha wolf will never mate with an omega wolf. However, there are cases where omega wolves rose to the rank of alpha wolves or left their pack and form their own, making them new alpha wolves. So yeah, an omega wolf will eventually mate an alpha wolf IF it's determine to be an alpha wolf

Actually, a male alpha wolf will mate with all females of the pack. This ensures that only the strongest male of a pack has offspring.