To get started, I normally do a:
cisco# show int acthis will show all of your routers interfaces, their descriptions, a note if they're disabled, and some packet counters. ie:
cisco# show int ac
Ethernet0
Protocol Pkts In Chars In Pkts Out Chars Out
IP 610356 115097881 742541 217076641
ARP 33830 2029800 8586 515160
CDP 0 0 32955 10018320
Serial0 sample.org T1
Protocol Pkts In Chars In Pkts Out Chars Out
IP 800831 209840619 631037 89882519
CDP 0 0 32954 9655522
Interface Serial1 is disabled
router#
Also a show version is helpful, and generally will tell you how much
memory is installed. On larger routers, show diag is availible which
shows information about all cards installed on the router.To view the running configuration, do a show running which is only availible on newer versions of IOS - to view the boot time config run show config - any time you change the configuration via the config command you will want to save your configuration with the command write mem.
Most of the 7000 and above series of routers have one or more thermometers inside which allow you to get various temperature readings - use the command show env all to view temperature and power supply information.