I've heard of boiling the parts if the person has certain medical issues, like Cystic Fibrosis, where they would need to be super careful of sanitation. But otherwise...my nebulizer instructions call for rinsing in warm soapy water (don't use the dish soap that has lemon in it), then rinse in warm water and drain. Do the vinegar soak at the end of the day. The vinegar is important because it helps keep medication and soap residue from building up...I get generic white vinegar by the gallon for this purpose.
The rep that set you up with the nebulizer - that person might also be a good resource. The gal that brought out my equipment/taught me how to use it explained the cleaning process.
I also have the Pari tubing set up (Incare? Nebulizer); if only they had adult size "animal" nebulizer masks! I've told my dh that breathing treatments might be more tolerable if I could do them wearing the "elephant" mask!