First we'll need to install Java 1.6 JDK, and be on PHP 5.2 or higher (You can check my PHP installation tutorial here. Also I'm on CentOS.
Install Java 1.6 JDK
yum install java-1.6*
Install Apache Solr
We're going to install Apache Solr into /usr/local/share; however you can install it somewhere else if you'd like (e.g. install it in the root dir / )
Download Apache Solr. We're going to use the latest version at the time of this writing: Apache Solr 3.5. Look for the latest version here: http://www.apache.org/dyn/closer.cgi/lucene/solr/