How to install MySQL workbench?

Run this command in Terminal (Ctrl+Alt+T):

sudo apt-get install mysql-workbench

Select "Ubuntu" from MySQL Workbench downloads page

You will have a choice of:

Ubuntu Linux ver. 10.10 (x86, 64-bit), DEB
(mysql-workbench-gpl-5.2.33b-1ubu1010-amd64.deb)

Ubuntu Linux ver. 10.10 (x86, 32-bit), DEB      
(mysql-workbench-gpl-5.2.33b-1ubu1010-i386.deb)

and 2 slightly older versions:

Ubuntu Linux ver. 10.04 (x86, 64-bit), DEB
(mysql-workbench-gpl-5.2.33b-1ubu1004-amd64.deb)

Ubuntu Linux ver. 10.04 (x86, 32-bit), DEB  
(mysql-workbench-gpl-5.2.33b-1ubu1004-i386.deb)

As you can see there are only 10.04 versions but you can download the .deb you need and when it is done downloading Ubuntu Software Center will open up with this screen:

and the rest is just normal Ubuntu. I needed it myself (mysql-workbench-gpl-5.2.33b-1ubu1010-i386.deb) so I can confirm it works.

Finally I found the easiest and direct way of installing MySQL Workbench on my 12.04 LTS.

(1) Simply install Synaptic package manager (from Ubuntu software center).

(2) Find MySQL Workbench under Database category (see the screen shot).

EDIT: As of August 2012, MySQL has released MySQL Workbench for Ubuntu 12.04, available here