Here is the guide to show you how to install SugarCRM Community Edition on Dreamhost share hosting plan.
Set up a new domain, subdomain, or folder for Sugar.
Set up a new MySQL database in Dreamhost Web Panel. Write down the mysql host name, user name, password and database name.
Download the latest Community Edition of SugarCRM. It is free version. Then, unzip into a folder such as /home/yourUserName/sitename.yourdomain.com/CRM/