MediaWiki Administrator's Handbook/User Block
User blocking is perhaps one of the most heavy-handed things you can do as an administrator, and the one that can cause the most damage. An administrator must therefore be cautious in using this power. Often a user will spend quite a bit of time building up a reputation under a particular user name, and by blocking that user they will not be able to edit from their account. Blocked users can still edit their user talk page (and user talk sub-pages?) unless these pages are protected and the user doesn't have sysop or higher privileges.
It is also possible to block IP addresses from being able to edit text. This does not stop a registered user on that IP address from being able to log in, but only stops anonymous users from using the edit functions. If there is a problem where a registered user is unable to access the Wiki due to an anonymous IP block, then the user must unblock that IP and reblock with anonymous users only checked.
Performing the Block 
The actual process of performing the block is rather straight forward. You can either go directly to Special:Blockip and get the page, or you can use your administrator's tools on the sidebar and then clicking on the Block User link. This is only visible when you are viewing either a user page or a user talk page.
All this does is simply fill in the name of the user account or IP address so you don't have to worry about misspellings or getting the wrong IP address.