This project, my first attempt at a tile mosaic, and a way of using up some surplus tile left after tilling the basement floor. The mosaic looks complicated, but is not. I installed it in the foyer of our bungalow (raised ranch) centered under a hanging lamp. In the following steps I will show you what I did, including a couple of mistakes I made, (hopefully not showing up in the above final product.)

To do this project you will need the following tools:

A wet diamond tile saw. (Purchase from Home Depot for about $50, or rent from a tool store.)
1 bag of tile cement referred to as Thinset
1 bag of sanded grout, colour to match adjacent tile
bag of plastic tile seperators (1/8 inch and 1/4 inch thickness cross shaped.)
A piece of wall board/ gypsum board/ plywood, measuring 40 inches square (big enough to hold insert.)
blank paper to cover the board and on which you will sketch your design
Protractor
Compass made from stick about 20 inches long
a roll of clear plastic shelf protector (sticky.)

Skill set required:
Do it yourself skills with no fear trying new methods
Patience, plus measure twice cut once attitude! You need this one in spades.

Step 1: The Design

I was interested in doing mosaics in general, so I spent a lot of time at the library reading about techniques, new and archaic. I also spent a lot of time on the internet checking out tools and materials and examples of mosaics both in design and implementation.
In the end I chose a design that could be implemented WITHOUTspecialty tools and which could be implemented using nothing beyond straight line cuts and 45 degree cuts on the wet saw. Last, but not least, I wanted a simple design that I could implement using my supply of left over 3/8 inch floor tile.
To be clear, mosaics are usually constructed from small pieces of material. In ancient Rome, the tiles termed tessara were made from cubes of limestone, typically 1" on a side. Nowadays, the tessarae are made from virtually any shape and size and material, including semi-precious and precious stone, glass, marble, and ceramic . However, the people who design and construct mosaics still tend to use pieces of 1" or less in surface area. THIS PROJECT IS MADE WITH BIG PIECES!
The design I am using is not original to me. I did change the design, including using BIG pieces instead of tessare, but otherwise the basic design is pretty generic. If you just love it and want to start producing these, please check for any copyright. This instructable shows how to construct, not how to design.
In order to build the inlay, I did a fairly straight forward analysis of the design. The pic here is from an AutoCad image I created simply by copying each element in turn using a repeat copy tool. The basics are straight forward, 36 outer elements into 360 degrees gives a 10 degree subtended angle, the 18 element set is twice that or a 20 degree subtended angle. The circumferances, are chosen arbitrarily but selected to give a pleasing pattern. The entire inlay uses a 1/8 inch grout line.

Step 2: Drawing the Circles

I did this project several years ago, so most of the photographs are missing. As a substitute  I am using several small sketches to get the idea across.
I decided on a 35 inch diameter inlay, since that was all the would fit on my piece of 40 inch by 48 inch piece of gypsum board. On this board, I placed 2 sheets of 24 inch by 35 inch presentation paper, taped in the middle to cover the entire board.
To draw the circles of the inlay, make yourself a compass from a piece of wood similiar to a yard stick, cut off at about 20 inches. Drive a 3 inch nail at one end and drill holes along the length of the compass at the various places ( given below) to accomodate a lead pencil.
Next find the centre of the inlay. Draw a line side to side on the paper. Draw a second line perpendicular to first. Draw all the circles using this intersect as your centre. To duplicate what I did, draw circles using the numbers below as the radius of each circle. You can alter any of these to suit your own requirements. I
used 7 circles.
rad1: 2-3/4 inch   rad2: 2-7/8 inch    rad3: 3-3/4 inch
rad4: 6-1/4 inch   rad5: 6-7/8 inch    rad6: 10-5/8 inch
rad7: 17-1/2 inch

Step 3: The Circles

The circles represent the TOP of where you align the cutout tiles and at this time do not take into account the grout.

Step 4: The Spokes That Define the Tile Pieces

Remember, the design has 36 outer elements at the outside of the inlay, 36 degrees divide by 36 is 10 degrees. The middle elements number 18 or 360/18 degrees = 20 degrees.
Use the protractor as shown here to mark the 20 degree arcs. Draw a line from the marks through the centre, extending the line from one edge of the design to the other. I used a yard stick.
For the 10 degree lines, repeat for the process by marking 10, 30, 40 degrees degrees. I found it useful to use a very sharp pencil and a different colour for the 10 and 20 degree lines.

Step 5: Completed Spokes

This is what it should look like. Now draw in the tile pieces, so that each tile piece will fill a segment in this drawing. Remember the grout lines have no thickness now, so when you draw each tile piece, allow 1/16 inch on all edges of the piece. (Recall the AutoCad drawing.)

Step 6: Draw the Basic Elements

The inlay uses a set of THREE colours. In my inlay, the centre of the design matches the colour of the surrounding floor tiles. This is a sort of sandy colour. The second colour is a grey-green colour that I used as a trim in the basement tile. The third colour I chose is a very dark grey, not used anywhere in the house, but contrasting nicely with the rest of the inlay pieces.
The diagram shows the basic design elements of the inlay. Recall the AutCad drawing as a guide.
To proceed, use a sharp pencil and draw lines inside the areas defined by the spokes and circles. This line should be 1/16 inch inside the defining area. This is 1/2 of the grout line. What I did was to draw these lines on a piece of tracing paper, to make it easier to transfer the lines to a piece of tile. When cut, this will be your pattern piece. When setting the saw fence remember the angle is 1/2 the angle of element being cut. Make lots of practice cuts!
Note that the angles on the pointed pieces are 45 degee angles drawn from the end of each tile.
As a guide on how to proceed. Label the tile circles from the outside in to the centre. there are 6 tile circles. So the first circle is the dark grey tile triangles. I would suggest that you leave these to the very end. Start with the second circle and cut 18 sandy and 18 grey-green elements using your pattern piece. Check frequently to see if the fit is good in the intended segment.
For the second set of cuts, cut the pieces for circle 4, the sandy coloured pieces. There are 18 of these.
So far there has been no reason to round the end of any tile pieces. This is because for the segments that fit in the 10 degree areas, the ends are a good approximation of the arc of the circle into which they fit.The pieces of the third circle are in a 20 degree arc segment, and the interface between the second and third circle will require rounding

Step 7: The Assembly

OOPS number 1! Here is a photo of how mine looked at the first set of cuts. Notice the grout seperators. Also notice (because I can't skip it) that the third circle of elements are all TOO SHORT. I recut them of course, but as a cross check cut the second and fourth circle pieces first and then cut circle 3 pieces. Note that these third circle segments have to be rounded to nest properly with the circle two elements. It is a good idea to round the bottoms first, before cutting the 45 degree angle on the third circle elements. (I know, I know; measure twice cut once.)
Rounding the bottoms of the third circle elements can be done on the wet saw by using the edge of the blade as a grinding wheel. You will need to do this with the centre circular piece as well.
When you try to fit all the pieces of any circle together, seperate each piece with a 1/8 inch spacer. When you do this the lines between each segment becomes parallel. This picture shows how the 20 degree pieces are forcing the fourth circle elements out of true.
The center piece is cut with multiple straight cuts until almost round. Finish carefully with the edge of the wet saw a a grinder

Step 8: The Completed Inlay

When all cuts have been made and checked that the tile pieces fit more or less correctly, the tile pieces are removed and a several overlapping pieces of clear shelf covering is stapled over the drawing STICKY SIDE UP. Now replace the tile pieces, pressing down on each in turn to hold them in place over the drawing. Test that the plastic spacers fit in the grout lines. When all looks satIsfactory, remove the spacers and cover the entire inlay with overlapping plastic shelf covering, STICKY SIDE DOWN.
NOTE CAREFULLY:
Later experience showed me that I should have used mesh backing over the drawing, again with sticky side up. In this way I could have applied the grout THROUGH the mesh before installing the inlay. I could have also stiffened the inlay by applying Thinset over the grout, which would have simplified the install greatly. Later I found that mesh used for taping gypsum wall boards was an excelllent and cheap source of mesh.

Step 9: Remove Some Floor Tile

Now the inlay is ready to install, I pulled up enough tile in the foyer to accept the mosaic. HOLLY COW! where is the underlay? Well some builders use MINIMUM building code as a guide and the minimum code doesn't specify underlay on Plywood. Oh well let's get on with it.

Step 10: The Install

Here is a shot of the Inlay ready to be put in place. I laid in about 3/4 inch of thin set, and pressed the inlay into the cleared area using a 2x8 inch board to assure the mosaic was level with the surface. Recall that as I implemented the inlay, there was no grout nor Thinset on the medallion. This was a mistake. The inlay was like a big flexible pizza when I installed it. I reasoned that there would be little adhesion between the inlay and the Thinset unless I squeezed the inlay into the niche in the floor. As it happened, this approach did work and I followed up using the gypsum board holding the drawing to flatten the inlay very nicely.

Step 11: Removing Thinset: the Morning After

Recall that later events showed I should have grouted the inlay from the bottom and stiffened the medallion with Thinset before installing.
This picture shows me paying the price as I carefully picked Thinset out of the grout lines. This took about two days of miserable grunt work. I did learn however, and if I get time I will publish an instructable showing a second inlay, using tessare and done in a more productive way.