Tile a Floor Cheaply

If you are willing to take some time, you can save money when redoing your floor.

Steps

Decide whether you want to make a uniform design with similar tiles or create a mosaic (https://en.wikipedia.org/wiki/Mosaic) with various types. It is much easier to find random tiles (broken and whole) and combine them in new designs than it is to have them uniform, but both can be had if you are patient enough.
Search construction sites. Commercial buildings all need to have bathrooms, and almost all bathrooms use a large amount of tile.
Contact tile contractors and asking about their left-overs from recent jobs or supply from jobs that fell through. Some will be happy to help as long as you haul it away yourself without their help.

This can be done before, after or during your tile gathering. Some people find it is easier to make a design with what they have gathered, while others are more comfortable finding tiles that match the pattern they have already made. Do what works best for you.
Geometric designs are a great way to make use of cut and left-over bits.
Lay out the tiles on the area that you are covering without adhesive. Use this time to gauge what looks best in practice.
Remember to leave grout space between the tiles for the grout when making your layouts. Smaller tiles have 1/8" to 1/4" grout lines, where large tiles can have 1/2" to 3/4" spaces for grout without looking awkward.
After you have settled on the design you want and have gathered and shaped the tiles you need, attach them as you would any tile floor - See related article for Laying Tile Floors for details.

When following the tiling directions in the related article, remember that being square is only necessary if you are using all perfectly square / rectangular tiles.
When working with contractors, the easier you make the situation for them, the more inclined they will be to help you.
Ask before you take, especially at construction sites. Unless the tile installers are present and you can ask their permission directly, this is not the best route. At any construction site, there are multiple contractors that are not related (electrical, plumbing, HVAC, etc.) and may not care whether you take something that does not belong to them or they mistake for trash.
Don't be afraid to use random and irregular sized pieces.

If the tiles are not of the same thickness, you can make some minor adjustments by changing the thickness of the mastic (adhesive) you use to set them on the floor. Adding more mastic below the thinner tiles can raise them up to the level of the thicker tiles; however, make sure to allow sufficient drying time for thicker layers of mastic.
Make sure the thickness of each tile is the same if you are making a mosaic on your floor.
Wear thick leather gloves to keep from getting cut. Cut tile is razor sharp. Even small pieces can do a lot of damage.