This is not a simple process.. If your text does not offer a good description. As good place to start reading is under Characteristics of Teleomorphs found in this http://www.mycolog.com/CHAP4a.htm. Aspergillus has a teleomorphic (sexual) as well as anamorphic (asexual) life cycle, both together comprise the whole life form or holomorph.
I'll attempt to condense the concept, in the following:
The teleomorphs exhibit a unique nuclear phenomenon called the dikaryon. After sexually compatible nuclei from different mycelia, have been brought together by anastomosis (fusing of two hyphae), these nuclei pair off, but don't fuse immediately to form a diploid (2N) zygote. Instead, they go on dividing to form what are called dikaryotic hyphae, in which each compartment (cell) has two sexually compatible haploid (1N) nuclei. These 2 haploid nuclei will eventually fuse after further development, into diploid (2N) nuclei which is followed by meiosis where the genome finally has the chance to be reshuffled (just like meiosis in ordinary sexual reproduction).
glossary:
hypha is threadlike fungal filament, (plural - hyphae).
mycelium is a mass of hyphae (plural - mycelium)