I made one for a laundry room. I made the top too. I used an old kitchen sink in the top to give us a laundry tub. Sorry I don't have pictures handy (Some handy guy I am)
I do not think the project is a great one to learn woodworking skills on. I started with all rough lumber, not what you would find at Home Depot.
Off the top of my head here is a partial list of tools I used.
Oscillating spindle sander
Wood probably cost me $50, maybe a little less, hardware (hinges, pulls) cost me maybe $30 or $40. Sink was "free" but cost me a couple hundred to replace the kitchen sink. The faucet cost me $150 or so.
I wouldn't pursue this to save money. You would want to go down this route if you have something very specific in mind and feel you can invest the time and money to do it correctly.
There is a great forum dedicated to woodworkers that I frequent. If you posted your question there I suspect you would get a similar response to mine.
I hope the next statement doesn't come across harsh. A woodworker will read your suggestions
My guess is to frame somthing with 2x4s to the proper size and cover it with some type of wood, stain it.
with some amusement. This certainly would not be the way a woodworker would build it.
If you go to http://www.forums.woodnet.net/ubbthreads/ubbthreads.php
and post your question I would suggest it say something like.
Hello - I am interested in learning something about woodworking and I have a need for a small vanity. I would like to tackle this as my first project. My experience is limited as are my tools. I have a (list wood working tools) and a desire to learn. (Then describe your project, attach some pictures or examples of what you have in mind, etc.) Any suggestions as to where to start?
You will get a lot of encouragement. Some discouragement (go buy something). Someone might steer you to plans. You may get suggestions on what additional tools you may need, etc.
email me as a reminder to take pictures of the one I built if you are interested. You can reach me through the link in my sig.