The instructions at the official site are a little verbose and hard to follow, so here's how I got Macaulay2 installed.

Note: It is probably best to reverse anything that you have already done and remove anything related to macaulay2, so that the method below will be successful and without errors.

The easiest thing is to put the Macaulay repository in a separate list file in /etc/apt/sources.list.d/. This is what I do with all external, non-Ubuntu repositories.

1) Create and open the list with

sudo nano /etc/apt/sources.list.d/Macaulay2.list

2) Now paste into that file the following (For future readers: substitute quantal for your Ubuntu version):

deb http://www.math.uiuc.edu/Macaulay2/Repositories/ubuntu quantal main

Save the file with Ctrl+O and exit with Ctrl+X.

3) Add the repository key with

wget -q http://www.math.uiuc.edu/Macaulay2/PublicKeys/Macaulay2-key -O - | sudo apt-key add -

4) Update your repository lists with

sudo apt-get update

5) As the official page mentions, you may need to install liblapack3gf as well before you install macaulay2:

sudo apt-get install liblapack3gf 

6) In addition, you may need libntl-5.4.2 if you are running Quantal (12.10) or later as it is no longer in that repository. I already had it installed, but you should be ok to install it from the Precise repos as listed above, but just choose the right architecture and use

sudo dpkg -i file.deb 

There are no dependencies to cause any concerns in this case. Other people running 12.10 have noted that this is also necessary.

7) Now install the program with

sudo apt-get install macaulay2 

Note: If apt-get keeps failing then download and install the correct files (Macaulay2 and Macaulay2-common) for your architecture manually from the repository and install each with gdebi so any further dependencies can be resolved.

8) The command to launch it is M2 (uppercase M) and the man page can be reached by entering man M2.