If you are looking for a cheap way to make a hard floor in a foyer, in a shed, or barn, you may want to consider a tamped earth floor, or what is called "tataki" or "douma" in Japanese. Japanese buildings have all historically been tamped earth or wooden flooring. Some temples have earth floors over huge areas. Kitchens and storage building floors were often made of the material that is cool in the summer and warm in the winter. Recently home builders have been returning the material for its aesthetic appeal, as well as the cost. The floors last for decades with moderately heavy use, are easy to repair if they crack, and can be made smooth or textured and decorated. They are inexpensive, because the materials are available nearly anywhere, and you can do all of the work. Finally, in the end the floors return to their natural condition, dirt.
First you need to consider how large an area you want to cover. If your foyer is three meters square, and you want a floor that is fifteen centimeters thick, then you will have to have about one and a half cubic meters of compacted earth and lime in the end product. I recommend at least fifteen centimeters of thickness for a strong floor. The thing is though that once this is packed down, it is about 1/3 the height of the original materials untamped. That means that you will need to start with about three times the amount of sand and lime to compact for your floor with the desired dimensions. In other words, you will need a little more than three cubic meters of sand and a one cubic meter of lime for your three meter square floor.
After you have calculated the amount of the simple materials you will need, you need to prepare the area that will serve as the base for the floor. The beauty of an earth floor is that you can easily put it right on top of what ever base you have, dirt or concrete. (You cannot make this on top of a wooden floor, because it will crack as the wood floor bends during tamping and after it dries.) If you are making a floor on a dirt base, then you need to also decide whether you want to have hard edges. For example, if you are making it so that your door will close, you need to make a frame that will define the dimensions of the floor so your door will shut. You can do that easily with a stout board cut to fit the width and desired height. If you are making a ramp into a storage facility where you may be rolling in your wheeled lawn tools, then you will need to dig a shallow ditch of about 10 centimeters in depth and the same in width, with the ramp ending at the middle of the ditch.
Mixing the earth mixture is easy enough if you are covering a rather small area, but if you are dealing with a large shed or indoor area, a backhoe may be useful for mixing. Mix the lime and dry river sand together, mixing it thoroughly. Do this right before you are ready to spread and tamp it, because the lime will start to react to any moisture immediately. You can then start mixing in water. You will need enough that the mixture is something like beach sand after the waves have retreated, damp, but water does not drip out when held in your hand. Start shoveling it onto the area to cover and start tamping it.
A tamper can take many forms. In Japan, a wooden mallet was used to tamp smaller areas, and a pine log with four long handles, like shovel handles, for two people to lift and drop was used for larger areas. Pine was used for its weight, but also for its auspicious characteristics in Japanese folklore. For those who are less interested in details or who have an area that is too much to be dealt with by hand, a gas powered tamper will work just as well. As the mixture is compacted, more should be added on top and tamped until it reaches the desired depth. What ever you do, you will have to use all of the mixture that you made that day. It will harden as a pile as the lime reacts with the water, and will not keep.
Once you have beaten it to the desired area and depth, you should decide how you want to finish it. If you want a rough finish, that is fine. The tamping should have left marks, and those may work. You may want to add different designs by stamping in a rope to make letters. Some people work in marbles, pretty rocks, or ceramic tiles. Or you may want to make it smooth. If you want a smooth finish, you will need to rub it with a mason's float or trowel. First sprinkle the area you can work on immediately with a little water from a brush. Try a small area first and work your way up. Then with the float, give a small area a beating, and start to rub it with the float. It works best if you lift the leading edge just slightly as you smooth the area back and forth and round and round. The fine, wetter particles will come to the top, and the coarser particles will be worked into the center of the floor. The fine particles with eventually make a smooth surface. If there are areas that are lower than others, fill it it with some of the left over mixture, and beat it into place with the float or trowel.
The floor will dry from the inside out, meaning that the outside will feel wetter when you touch it that it really is on the inside, but you shouldn't let it dry too fast. You will have to avoid walking on it for some time. If you can give it a month, that would be best. If you live in a dry area, cover the floor with a grass mat and sprinkle it with water daily, just so keep it from drying so fast that it gets flaky or crumbly. If you live in a damp climate, like Japan, you will need to keep areas under a roof damp, and areas outside from washing away if there is, for example, a water drain coming off of the roof. After about a month you can use it normally.
As the years pass your tamped earth floor may develop cracks or wear out in spots. Just mix up a little soil, lime and water and pound it down, let it dry, and it will be good as new. If you sprinkle it with water from time to time, it will thank you, too, especially in dry indoor areas. Some people in some areas of the world put oil on their dirt floors. You may want to try that, too, but choose a non-petroleum oil with a smell that you can live with, especially if it will be in your living area.
Earthen floors have been used all over the world for millennia in all kinds of spaces. There are different details in the mixtures. Some places even mix ox blood into their mixture, but what they all have in common is that they use naturally occurring materials to make low maintenance floors that live and breath with you and the rest of your space. They are easy to make, even the kids can be involved in the process. (Keep them away from the lime!) They are beautiful and soulful to live with.