Sodium iodide is a salt with molecules consisting of one atom of sodium and one of iodine. Its formula is NaI. Sodium iodide forms easily from its elemental components and the reaction releases a lot of energy in the form of heat. The compound is extremely water soluble. Sodium iodide itself isn't dangerous, unless you ingest large quantities. Small amounts are used in medicine as iodine supplements or, in radioactive form, as a treatment for thyroid cancer. Iodised salt contains small amounts of sodium iodide added to the table salt.
Put on lab coat, goggles and gloves. None of these chemicals are poisonous, but elemental sodium will eat through your skin and the reaction may spatter as it proceeds.
Place iodine into the borosilicate glass container and move the container to a well-ventilated, heat-resistant location. A lush lawn or driveway work well. According to basic chemistry, one mol of sodium (23g/mol) will react with one mol of iodine (127g/mol), but add extra iodine to compensate for what will escape as gas.
Cut an appropriately-sized piece of sodium and wipe off as much oil as you can. Place the sodium on top of the iodine crystals. The reaction between the iodine and the sodium releases so much heat, you may see the sodium melt. Iodine will escape as a purple gas; try to avoid breathing it.
Stir the sodium and iodine mixture if the reaction weakens. Repeat as necessary. Try to ionise all the sodium in the container. Surplus iodine is not a problem. The sodium iodide will appear white as it forms. You may also have surplus iodine or residue from contaminants. Allow the container to cool to room temperature.
Add water to the container until all the sodium iodide and iodine are dissolved. If you have unreacted sodium left over, the water may bubble and spatter as the metal converts to extremely corrosive sodium hydroxide.
Boil off almost all the water. As the water boils, the excess iodine will leave the solution as a gas, so do this in a well-ventilated place. Once you have boiled the solution down to a slurry of water and crystals, add more water so everything redissolves.
Add vinegar to the solution until the solution reaches pH 7. The vinegar will react with any sodium hydroxide to produce sodium acetate and water.
Cool your solution. You should see crystals form as it cools down. The crystals are sodium acetate. Sodium iodide is about twice as soluble as sodium acetate, so the latter precipitates out of solution first. Either remove the sodium acetate or decant the solution into a small pot or other heat-tolerant vessel.
Boil off the water. The crystals that form should be reasonably pure sodium iodide. Sodium iodide is hygroscopic, meaning it absorbs water. You may not be able to get the crystals bone dry.
Always wear safety gear. Some of these steps are dangerous, if you're careless. Ensure there are no flammable materials around your work area.