To Remove Friends - or more specifically "Relationships"
Log into your facebook account via: http://www.facebook.com/
Click "Account" from the top right hand side of the header, and select the first option "Edit Friends". That will take you to your editable friends list: http://www.facebook.com/home.php?#!/friends/?ref=tn
Select the "X" next to the friend that you wish to remove.
*Note that you will be removing the connection between you and the friend, and not the actual friend. In other words, you are deleting the "friendship", not the "friend" (read: You can't delete other peoples facebook profiles).
To block friends from ever seeing you again:
Go to "Privacy Settings" in the account link: http://www.facebook.com/#!/settings/?tab=privacy&ref=mb
Select "Block Lists" from the bottom of the page.
From there you can add names and emails of people you want to block.
More Resources
There are a number of other things you can do to manage relationships w/ people. For instance I like to leave people as friends, however add them to specific "lists". That way only people on specific lists can see my posts, pictures, etc. I can also chose which list to share with when I post, or chose to share with all.
All this is outlined in the facebook help center under the "friends" topic: http://www.facebook.com/help/?page=441