Here's a quick and dirty on installing the latest (version 6.5.0-0 as of this writing) ImageMagick on Ubuntu 8.04.

Start by removing any old versions previously installed via apt-get:

sudo apt-get remove imagemagick

Then update apt-get and install some supporting packages:

sudo apt-get update
sudo apt-get install libperl-dev gcc libjpeg62-dev libbz2-dev libtiff4-dev libwmf-dev libz-dev libpng12-dev libx11-dev libxt-dev libxext-dev libxml2-dev libfreetype6-dev liblcms1-dev libexif-dev perl libjasper-dev libltdl3-dev graphviz gs-gpl pkg-config
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Use wget to grab the source from ImageMagick.org.

Once the source is downloaded, uncompress it:

tar -xzf ImageMagick.tar.gz

Now configure and make:

cd ImageMagick-6.5.0-0./configuresudo makesudo make install

To avoid an error such as:

convert: error while loading shared libraries: libMagickCore.so.2: cannot open shared object file: No such file or directory
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Add the following line to ~/.bashrc:

export LD_LIBRARY_PATH=/usr/local/lib

Update: If you still get an error like the one above, try running ldconfig:

sudo ldconfig

You can confirm the install and available formats with:

identify -list format