Vim has a certain infamy for having a relatively high learning curve compared to other editors. While this may not be completely undeserved, learning the basics of how Vim operates will make basic editing in Vim much less daunting than it may initially appear. A good deal of what's below may be duplicating resources already available on the internet, but a little bit more knowledge shouldn't hurt (and it just seems silly to have these other pages about Vim without giving you some basic usage instructions). So don't expect this to cover everything you might possible encounter or need, but it should get you over that initial learning curve. Also try out the vimtutor program that comes with Vim. It could make this whole page unnecessary.
One of the first things noticed by many new users is their inability to type into the current document upon opening Vim. I would guess that this little surprise is probably responsible for most of the confusion and allegedly high learning curve, but for slightly deeper reasons than this simple initial state.
Vim operates in modes, as opposed to most other text editors, which are mode less. For example, in MS Notepad or MS Word, you can simply type wherever you wish and run commands with shortcut keys or by clicking items with your mouse. In contrast, Vim separates these functions into multiple modes, which are simply different states your editor can take. The default mode on startup, normal mode, allows you to type different keyboard shortcuts that we'll discuss shortly. By typing a colon in normal mode, you'll enter into command mode, which is used for various commands, searching, find and replace, and more. Finally, the mode that most people want is insert mode, which you can use by typing an "i" while in normal mode.
There are a few other modes that you'll encounter, some of which may be detailed below. For a more comprehensive list, look up modes in the Vim documentation.
Before you can adequately experience navigating the text, you'll need some text to navigate. If you haven't already, press i to enter insert mode and type a few lines of text. When you are done, you can press ESC to return to normal mode.
Now that you have some text and are back in normal mode, try using the h, j, k, and l keys to move the cursor around the text. Your arrow keys will also work, but I generally prefer to use the hjkl keys because they are already under my fingers on home row. (If that last little bit was Greek to you, then I suggest you find a good typing tutorial and learn to touch type. It will increase your productivity greatly regardless of the editor you use.)
A few other useful combinations for normal mode:
While in normal mode, you can enter command line mode multiple ways, but for generic commands you will use a colon. Some useful commands are listed below. I've included the leading colon to differentiate those commands from commands that are entered by other characters.
Many of these commands, notably those related to editing, writing, and quiting, will fail for various reasons. For example, if you have unsaved changes to your current file, Vim will not allow you to exit or edit a new file unless the changes are saved. You can work around this by putting an exclamation point after the command. :q! will quit the current file without saving any changes. The other commands use the exclamation point similarly. Also note the combination commands like :qa and :wq. As you might guess, there's also a :wqa to write all files and quit Vim.
These are only a very small fraction of available commands, but they should be enough to get you started editing. Browse through the help files occasionally and check out the Vim Tips pages for more useful tools.
Visual mode is like normal mode with one noticeable exception: moving your cursor highlights ranges of text instead of simply moving around the screen. Enter into visual mode by hitting v, or into visual line mode by hitting V. Visual line mode is exactly like visual mode, with the exception that you select entire lines instead of only ranges of characters.
While in visual mode, you still have access to many of the commands from normal mode, such as x (cut), d (delete), c (change) and p (paste), which will now operate over the highlighted range of text. Note that if you paste while selecting text in visual mode, the highlighted text will be pasted over, much as you might expect.
This guide is far from exhaustive, but I hope it will help you get started using Vim more efficiently than you would have just stumbling around, trying to guess why things weren't going the way you thought they should. I'll wrap up here with a few commands that I find fairly useful that weren't already covered above.