Uranium is a metal; like iron, we dig it out of the ground. The U.S. used to mine most of its own uranium, but now about 75% of our uranium is imported, mostly from Canada. Until recently, an ecologically dirty but inexpensive process similar to that used for mining iron was used.
Machines and men dig gaping pits into the ground and haul up the uranium ore and dirt. The ore is washed with water and then refined(milled), leaving a brownish yellow powder that is relatively pure (90%) uranium oxide and a slurry of water and radioactively contaminated rocks and mud known as mill tailings. These tailings were generally dumped at the mine sites, leading to the awful tragedy on many Navajo reservations. Their ill effects continue to this day; these tailings leach both heavy metals and radioactive particles into the groundwater.
The yellowcake is milled further, leaving pure uranium oxide. This oxide can then be formed into rods for use in some civilian reactors, enriched and formed into rods or pellets for use in other civilian reactors, or converted into its metallic form and highly enriched for use in weapons and military reactors. See how to enrich uranium.
The modern mining method is the very model of environmental conciousness. As uranium is usually quite well isolated from the water table while it is still in the ground, in-situ leach mining simply leaves the uranium where it is and exploits its unfortunate tendency to leach into groundwater. An acidic solution of water and sulfate is normally used, but if there are significant deposits of alkaline chemicals such as calcium in the ore, an alkaline solution of water and carbonate is used instead. This solution is injected(pumped down) into the orebody from a grid of wells spaced about 90 feet apart and extracted from wells in the center of each group of four injection wells. The mining area is carefully monitored to prevent the mining solution from carrying uranium into the water table, so in-situ leach mining is quite safe environmentally. It leaves behind no mill tailings and no slurry; no workers are exposed to radon or heavy metal aerosols. ISL mines are rapidly replacing earlier open-pit mines.
ISL mines produce uranium peroxide, which is easily reacted to form uranium oxide or uranium metal. Although they cost more than open-pit mines, they endanger neither their workers nor the environment. In our modern world, in-situ leach mining is the way to go when we need uranium for our clean, cheap, and efficient nuclear reactors or nuclear weapons.