Raspbian runs Avahi services, which means the computer can be discovered automatically using the Zeroconf system (Bonjour, Avahi, etc.)

If your raspberry pi is named DRAWS-CALLSIGN, then you should be able to access it from other machines like this

ssh draws-callsign.local

or

http://draws-callsign.local:8080

as long as the computers are on the same LAN.  Bonjour is built into most Apple products, Avahi/Zeroconf in many Linux/Android systems. If your Windows box doesn't have it, install iTunes.