How many souls can I store in the Black Star to do enchanting?

I got a Black Star and I've read that it's supposed to be like an infinite black gem.

I would like to use it for enchanting.

How many souls can I carry in it?
Just one at the time?

I guess when I'll be using it to perform enchants, it won't disappear but just become empty, right?

Solution 1:

The black star is an infinite soul gem with the power to capture any soul, either from an NPC or a creature.

It functions exactly like a normal soul gem, only one soul at a time. When you use it to charge or enchant an item, it will not disappear, it will just become empty.

Solution 2:

Lets answer your question(s) one at a time.

How many souls can I carry in it?

Just one.

Just one at the time?

Unfortunately yes.

I guess when I'll be using it to perform enchants, it won't disappear but just become empty, right?

Precisely.

The Black Star has two states: Empty and Filled with [inset soul level here]. Since I tend to have a bunch of petty through greater soul gems on me at all times I don't have to worry about storing deer or elk souls in my Black Star (what a waste that would be). In Skyrim souls will be stored in the lowest leveled compatable empty soul gem in your inventory confirmed here.

If an empty Soul Gem is available in your inventory, then the soul will fit into the smallest Gem available...

For more information about soul gems, the black star, enchanting and soul trapping see this link. At the bottom of the linked page, under "See also", you will find the additional links.