Apache Solr is one of the most important peaces of software for a Drupal app with lots of content.
You can run Solr on a dedicated server of side by side with you LAMP stack.

To install Solr, first check which version of java is installed.

which java

If Java is not installed, check the available versions of Java and install the latest stable version. In my case it is 1.8

yum list available java*
yum install java-1.8.0-openjdk.x86_64

To verify the installed java installation

which java
java -version

The Apache Solr installation needs a solr user, let add one

adduser solr

Now download Apache Solr in the opt folder and run the install script

cd /opt
wget http://archive.apache.org/dist/lucene/solr/5.5.4/solr-5.5.4.tgz
tar zxvf solr-5.5.4.tgz
cp /opt/solr-5.5.4/bin/install_solr_service.sh .
rm -rf solr-5.5.4
./install_solr_service.sh solr-5.5.4.tgz

It is important that Apache Solr starts automatically when de server is rebooted.
With the first command you add solr to the startup config, with the second you can check if the settings are valid.

chkconfig --add solr
chkconfig | grep solr

Now that the Solr server is up and running, we are going to create an core instance. The simpelst way to do this is by using the solr scripts. It is important to run the script as the solr user. Otherwise it can't create the new instance.

cd /opt/solr/bin
sudo -u solr ./solr create -c corename

Congratulations. Your Solr server is finished!

It is important to make your installation secure. By default is the Solr admin interface available on port 8983.
Make sure this port is not open on your server. The easiest way make the Solr admin interface available in a safe way is to use Apache as a reverse proxy. Here you can configure SSL and basic authentication much easer than in Jetty (the Solr web server).

Setup Drupal Solr config

To make the installation complete for Drupal, you have to setup a Drupal specific configuration. Fortunately, the search_api_solr module supplies some excellent config files.

cd /tmp
wget http://ftp.drupal.org/files/projects/search_api_solr-7.x-1.11.tar.gz
tar zxvf search_api_solr-7.x-1.11.tar.gz
cp search_api_solr/solr-conf/5.x/* /var/solr/data/corename/conf
sudo chown -R solr:solr /var/solr/data/corname
rm -rf search_api_solr-7.x-1.11.tar.gz search_api_solr