Building from source is covered on their website as people say above, but the Bio-Linux developer keeps the fastx-toolkit updated and installable with apt on systems that support it, either through using Bio-Linux as your OS or installing packages on (for example) Ubuntu.
All you need is:
sudo apt-get install fastx-toolkit
You can see all the bioinformatics packages available from Bio-Linux here: http://nebc.nerc.ac.uk/tools/bio-linux/package-list
EDIT: If you don't have sudo privileges you can install locally without the sudo command.