IOS commands to look at what's there and how it's configured.
but no changing anything.
(from any mode, preface the show command with 'do')

User exec mode:

show version                (memories, IOS version, HW&SW, interfaces)
show flash                  (what's in flash)
show clock                  (time and date)
show arp                    (arp cache)
  show ip arp                 (same)
show hosts                  (static hosts, cached names?)

ping  hostnameOrAddress  [source INT]      (connectivity check)
traceroute  hostnameOrAddress  
telnet  hostnameOrAddress      (login to another router/host)
  ctrl-shift 6 then x  suspends telnet
  <cr><cr>  resume telnet 

  show sessions                (logins to other hosts)
  show users                   (connections to here)
  show whoami

show ip interface brief    (#1 basic info)


show ip route               (the routing table: connected,
                             static, dynamic routes)

show protocols             (routing protocols per interface)
show ip protocol           (routing protocols information)
show ip ospf|eigrp neighbor

show cdp                   (status of CDP)
show cdp neighbors         (info about neighboring Cisco devices)

show ntp status|associations
show snmp

show tcp                     (TCP connections)

sh terminal
sh line


Privileged/enable mode: (superset of user mode)

show running-config         (actual active configuration now)
show startup-config         (initial configuration at bootup)  

show interfaces [name]
show interfaces [name] accounting



show ip traffic     
debug ip packet


show ip nat translations          NAT
show ip nat statistics

show access-list                  ACL


show dhcp server       #what DNS server this access router uses
show ip dhcp binding   #leases given out by this DHCP server