You'll want to install the Universal forwarder on each linux server. Then set up a monitor for the log files (/var/log/ folder) and forward to the indexer. On the indexer you'll need to enable receiving in the manager. See our docs below.
http://docs.splunk.com/Documentation/Splunk/latest/Deploy/Aboutforwardingandreceivingdata http://docs.splunk.com/Documentation/Splunk/latest/Data/Monitorfilesanddirectories