setting up syslog on cisco router

Send commands typed to syslog
archive
 log config
  logging enable
  notify syslog contenttype plaintext
  hidekeys

Send debugging logs to syslog
Send our origin id as our ip
Set facility to local0
Set source interfaces to gig0/0
Set logging host IP address of the syslog server
Switch logging on for all destinations
logging trap debugging
logging origin-id ip
logging facility local0
logging source-interface GigabitEthernet0/0
logging host x.x.x.x
logging on

Make sure your have routes to your syslog server
Also firewall rules, you need syslog (udp 514 open)