Learning vi or vim is not easy. But it doesn't have to be that difficult, either. It is, in any case, faster, more powerful, and more productive than editing with any other editor, so you would do very well in investing the time and effort to learn it.
Being a vi lover myself, I came up with the idea of providing a graphical cheat sheet for those learning vi or vim, and I also found out it was a very good way to structure a tutorial. Here are the results for your learning enjoyment (or your colleagues').
By the way, I recently published the definitive article explaining why vi/vim editing is so much better than regular editing. It should prove useful if you want to read it yourself, or if you want to point your skeptical friends to a description of why it makes sense, apart from being an entertaining read: Why, oh why, do those #?@! nutheads use vi?.
Graphical cheat sheet based tutorial
The tutorial above is structured in 7 lessons that cover the major commands in vi/vim. They are structured so that you will learn the simplest and most useful first, and the more advanced ones afterwards. Actually, using just the commands shown in lesson 1, you can already start editing in vi/vim in a similar way to how you would on a regular editor. Lesson 2 introduces the very powerful, and vi/vim-exclusive operators, and the rest of the lessons advance from there. Each thumbnail links to a high-resolution bitmap version. You can also download the full tutorial in a single zip file with all the bitmaps or a single zip file with all the SVGs (see the note above about incorrect rendering on Firefox).
Notes
vim is an incredible editor by Bram Moolenaar, based on the original vi by Bill Joy, adding a ton of improvements over it. Nowadays, you should choose vim over vi every time you can.
The cheat sheet and tutorial cover most important functions of vi's input model, leaving out the more advanced regular expressions/ex command line material. This should be a very good beginning to becoming a vi/vim wizard.
With the single exception of the external filter feature ("!"), all functions shown are supported by ViEmu, my commercial add-in that provides advanced vi-vim emulation in Visual Studio.
Relevant links
This cheat sheet has proven to be pretty popular. Here are some relevant links:
Sebastian Feltel prepared a version for the German keyboard layout
Brendan Kidwell prepared a PDF version for easy printing of the whole tutorial and cheat sheet
Peter Hosey prepared a Dvorak layout version
Donglu Feng prepared a simplified-Chinese version
G. Richard Bellamy took the time to prepare a Kinesis-Ergo style Dvorak version in SVG (for which he prepared a new Dvorak SVG version.
Bohdan Zograf prepared a very polished Belorussian translation
And of course, the article detailing why vi/vim editing is 'the killerest':