I bought a house about 2 months ago and had to re-do the bathroom right away on a tight budget. I saw some inspirational vessel sink designs online that I thought "hey, anyone can do that" ... and so here it goes.
Step 1: Materials
1) Desk or Table -- This is the key to the project. About a 2 years ago I bought this nicely detailed desk on Craigslist for $50 dollars. The important part for you is to find one that you don't mind destroying (you have to cut it up, drill holes, etc) and the right size and height. The height can vary depending on personal preference, but a good level is about 34 inches for me.
2) Vessel Sink -- This new trend made the whole project possible. You can find these at one of those big box stores, but I recommend eBay. I got mine for $75 dollars (including shipping) and it shipped and looks perfect. The seller I bought from is below. Any seller will probably be good, just make sure they have high ratings.
3) Facet (for Vessel Sinks) -- And now buy one of the all-in-one sink facets. They range in price from $40-190 -- Mine was around the $50 mark. I bought mine on amazon (link below). Make sure that it's tall enough for a vessel sink and remember that you'll want the handle up high. You don't want to reach around the sink to turn on the water.
Step 2: Installation of the Sink
To prep the desk/table you'll want to mock up the sink and facet first. Make sure you have them spaced correctly and that everything feels like it's in the right spot. Note there are some rules here on distance bowl should be from the edge, etc. But for me, It was all about how it feels.
First - Mark the exact center of the piece. Always measure twice, cut once! Now take a hole saw bit and drill in the correct size hole for the drain. Mine had to be at lease 1-1/4" so I went to 1-1/2". This part will take some problem solving if you have a drawer here. I took it out at first.
Second - Assemble the sink per the instructions that came with them. Mine came with a free pop-up drain, so there was nothing too hard about this part. Ensure that you have the water tight washers in the right spot, otherwise the sink could leak making you disassemble everything.
Last - Have a dry run. Put the sink in place and make sure you like how everything fits.
Step 3: Installation of the Facet
This part will vary from facet to facet. Mine was fairly easy. It had two screw-in water lines that hooked right up to the wall and into the facet.Make sure you use that plumber's tape here on the treads prior to assembly.
I used smaller diameter hole saws for the flexible water lines and a normal drill for two mounting screw holes. To fix the piece in place, there was a metal plate with two screws that put that basically put a vice on the table top to hold the facet still.
Step 4: Final Assembly and Installation
Now that the vanity has a facet installed and hole for the sink, you can install the sink for the last time. At this point you can fix the sink in place in a few ways - glue or braces. I used wooden blocks on the inside of the sink body to brace it in place (just in case I need to disassemble at some point).
Last step is to tie the vanity down some how. This is important to disallow the piece from moving.
You can now run the drain pipes and the hook up the waterlines. Here you will have to get creative to save some of the drawers/etc. I used a jigsaw to cut out space where the pipes were and simply re-installed the drawer for use.