press T on computer. Use your headset on Xbox live. You most likely will be booted if you lack a headset, as no one likes the poor kid who can't communicate.
!!! How to fix chat history / messages log in Borderlands on PC:
Find the file "C:\Documents and Settings\YOURUSERNAME\My Documents\My Games\Borderlands\WillowGame\Config\WillowGame.ini "
Open the file with a text editor (Something like notepad works great) and find the line "DefaultMessageDuration=7.0". Change the "7" to the number in seconds you want messages to be displayed. (Use Control+F to open the Find Box and search for "defaultmessageduration" to find the line you want easily.)