There are large conversion plants in the United States, Canada, France, United Kingdom, and Russia, along with smaller plants in Argentina, China, and Iran.
There are two processes used for conversion, the 'wet' and 'dry' processes. The main difference between the two processes is the way impurities are removed from the yellowcake. In wet conversion, impurities are removed through solvent extraction. The dry process does not use liquid solvents but instead removes impurities in the final fluorination stage (as described below). Almost all conversion plants use what is called the ‘wet process'. This starts when a chemical process involving nitric acid is used to separate any impurities from the uranium yellowcake (U3O8). The purified substance is then dried and mixed with hydrogen and nitrogen to create uranium trioxide (UO3).

In this two-step process, the uranium trioxide (UO3) is first heated with hydrogen fluoride to form uranium tetrafluoride (UF4). In the second stage, the UF4 is heated with fluorine to form UF6 gas. The UF6 is pressurized, cooled, and through condensation turns into a liquid. The product is stored in cylinders and converted into a solid crystallized form by further cooling it. Once in a solid state, the UF6 is ready for shipment to enrichment facilities.
Below is a soundless animation of the uranium conversion process created by the Cameco Corporation who runs a large American conversion plant. As you can see, the conversion process has quite a few steps and is rather complex.
In the next segment of Nuclear 101 the process of uranium enrichment will be discussed.
Sources:
Areva
Argonne National Laboratory
Nuclear Regulatory Commission
Presentation by Lisa Loden of Oak Ridge National Laboratory
WISE Uranium Project
World Nuclear Association