Here are some of the more common things you might wish to do with an editor, with the commands to accomplish them in Vi. Naturally, all of these assume command mode.
Search for a word using slash: /word or backward using question: ?word
Search again for the same word: n
Search again, but reverse direction: N
Go to particular line. Type the line number and hit capital G: 20G
Go to the end of the file. Use G without the line number: G
Delete some lines of text. Type the number of lines to delete followed by dd: 3dd
Paste some previously deleted text: capital P to paste in front of the cursor or little p to paste after.
Search for word1 and replace with word2 (note: this is a colon command): :%s/word1/word2/g
Undo an edit: u