When items are quarantined, they are put into a "vault", where they can have no interaction with your Operating System.
They are basically just sitting there, with no where to go.

They are stored in what's called Archives.
Each one has a date next to it, that corresponds to the date you quarantined them.
The quarantine list can be found by opening Ad-aware, and on the main page, click
Open quarantine list, located next to the
Objects quarantined entry.
Whatever Ad-aware finds, quarantine it.
If after a couple of weeks, your computer shows no adverse affects, it's safe to delete the quarantined items.
To do that:
Open Ad-aware, and click
Open quarantine list.
In the window that opens, click the Archive that you want to delete, to highlight it.
Right-click, and select
Delete Archive.
If you have questions about an entry, you can ask about it here, or Google it.
If it's something you need, for another program to function properly, you can add it to the
Ignore list, so in future scans, it won't be flagged as a problem.
To do that:
After the scan is complete, locate the entry.
Right-click the entry, and select
Add Selected to Ignore list.
If you've mistakenly quarantined something you need, you can remove it from quarantine.
To do that:
Open Ad-aware, and click
Open quarantine list.
In the window that opens, click the Archive that contains the entry you want to restore, to highlight it.
Right-click, and select
Restore Selected.
This will restore the entire Archive, even the bad entries.
Re-scan with Ad-aware, in the results list, add the entry you wanted to restore to you
Ignoe list, and quarantine the rest.
If you find that you've mistakenly added something to your
Ignoe list, you can remove it.
To do that:
Open Ad-aware, and click
Open ignore list, next to the
Objects in ignore list entry.
In the window that opens, put a check next to the item you want to remove from the list, then click the
Remove button, at the bottom.
Alternate Data Streams defaults, are fine.
I hope this helps, and I didn't confuse you more, than you already were.