If you make a lot of downloads outside of the iTunes Store, the songs in your library can be shuffled, leaving you with duplicate albums. If you want to know if you've downloaded twice, it's easy to find out in iTunes.
Show duplicate items in iTunes
Open iTunes from the Dock or from your applications folder. In the File menu of the top menu bar, hover over "Library" and select "Show Duplicate Items" from the drop-down menu.
This will display a list of items that share the same name and artist, so two songs of the same name by different people will not be displayed here.
The album, the duration and the content may be different, which may cause some confusion. Not all items on this list are offenders. You do not have to delete everything.
For example, compilation albums and "best of" collecting songs of this artist will appear here if you also have the original copy. If an artist publishes an updated version of a song on a later album, this also appears here, assuming that it bears the same name. "Premium" editions of albums with additional songs will also show here if you have both versions. In each case, you may want to keep some of the songs claimed by iTunes as duplicates. So check twice before deleting anything.
However, you never want to select and delete everything, because this list shows both copies of the song. You must hold down the Command key to select multiple items and manually click on each song you want to discard.
It's annoying, but there's no faster way to take into account all the possible reasons you'll have duplicates. Once you have selected everything, you can right-click and select "Delete from Library" to delete the items you have chosen.
At the top of the screen, you can change the view mode to "Same Album", which reduces it a lot more and solves most problems related to separate albums.
The items in this list are likely import problems and you can usually delete most duplicates without any worries.
If you want to keep duplicate songs, but change the album in which they are contained, you can do it with bulk editing. Select multiple songs that you want to edit with Command + click, then right-click the selected items and click "Get Info" on the shortcut menu.
This will bring up a prompt informing you that you are trying to edit multiple items. You can press "Do not ask me again" to hide this in the future.
Click "Edit Items" to access the information screen. From there, you can edit one of these boxes and they will be applied to all the songs you have selected. If you change the album, the songs will be sorted into a new album, although you may have to add the album artwork to "Artwork".
Be careful when editing information here, as it is difficult to put everything back in place if you mess up something. Track numbers, which you can not edit en bloc, are a disadvantage. If your track numbers are not in your place, you will have to edit them one by one manually, which may take some time.