I am trying to make some new Settlers tiles and would like to know what is the best method to make Settlers like tiles that are roughly the same size and thickness to standard settlers tiles with a custom printed image.
If you have access to a die-cutting press, as many teachers might, one can buy a hexagon press die.
Google Sizzix/Westminster Bigz Dies Hexagon and you find several sizes.
They make a block of 6x 3/4" and 1" hexes (suitable for counters), and one of 4x 2" hexes, and one which does 2.5" hexes.
Check your local craft stores and school supply stores.
The presses run from $50 to several hundred dollars, and the dies $20 to $50 apiece, so this is not an inexpensive solution. Nor is it efficient; you'll need to manually line up the graphic. It will, however, allow for leather, magnet, chipboard, and other non-paper samples to be easily made in a regular size.
Using them without a suitable press requires a firm hand, a smooth hard surface, and a rolling pin that can take your weight...
Best is a factor of both cost and volume. If you're like most hobby board game prototypers, then you're looking for a low cost solution, and you'll be making only a handful of tiles. For this, the manual process is best. This involves buying cardboard of the appropriate weight, printing your tiles with an inkjet printer, gluing the paper to the cardboard, and cutting it out with an x-acto knife.
You should be able to find everything you need from your local hobby store (bring a settlers tile to the store to find the kind you need). You'll want something that's just a tiny bit thinner than the actual settlers tile, because of the paper and glue. I suggest a spray adhesive, since it's easier to apply evenly.
After printing your image onto the paper, tape it taut, face-down on all four corners to a larger piece of cardboard first, then apply the glue, and finally the cardboard. Since the cardboard is heavier this will prevent unwanted bubbles in the paper. Start from the middle and apply even pressure in increasing concentric circles (some people suggest using a spoon, I use my fingers just fine).
If you're wanting multiple tiles, you can obviously do as many as you can fit on the paper at once to save some time.