From OpenLiteSpeed Wiki
We offer repositories for CentOS 5, 6, and 7. A user has also created a repository for Debian Wheezy.
CentOS 5, 6 & 7
Add the Repository
Use the following commands to add our CentOS repositories:
rpm -ivh http://rpms.litespeedtech.com/centos/litespeed-repo-1.1-1.el5.noarch.rpm
rpm -ivh http://rpms.litespeedtech.com/centos/litespeed-repo-1.1-1.el6.noarch.rpm
rpm -ivh http://rpms.litespeedtech.com/centos/litespeed-repo-1.1-1.el7.noarch.rpm
yum install openlitespeed
The above command installs the latest version of OpenLiteSpeed.
Using version numbers, for example
yum install openlitespeed-1.2.1, will install older versions. 1.2.1 is the oldest version in the repository.
Note: The OpenLiteSpeed packages in our repositories have SPDY enabled. The binary also includes the OpenSSL library needed to run SPDY. You do not have to install OpenSSL 1.0.1 to use SPDY if you download the package from the repositories.
Note: To prevent users from mistakenly upgrading to a beta version, OpenLiteSpeed 1.4 has not yet been added to our repository. It will be added when it is no longer beta.
OpenLiteSpeed will run automatically after the installation. A sample site should be running on the server.
To access your site, point your browser to http://[address]:8088/, [address] being the IP address or domain name of your web server machine. Use "localhost" if the server is on the machine you are using. By default, OpenLiteSpeed runs on port "8088".
A congratulations page linked to other testing pages should load into the browser when pointed to the above address. If not, try testing the WebAdmin interface. The default port for the WebAdmin console is 7080. Plug https://[address]:7080/, into your browser to go to the WebAdmin interface. Remember the "https://" and that for [address] you can use "localhost" if you're currently using the machine the server is on. A login page should load. The defaults for the administrator's user name and password are "admin" and "123456". For detailed information regarding configuration, please refer to our Configuration Guide, or click the "Help" link at the top of each page.
Stefano Balocco has created a Debian Wheezy package of OpenLiteSpeed in his repository. (Thanks, Stefano!) You are welcome to try it out, though we make no guarantees about its efficacy or safety.