Have a vintage French "laveuse" which for a better description is a boiling pot that showers contents with water, rather than merely letting them sit. However have simply boiled items in a stock pot before.
One thing to remember one normally boils laundry that is already clean or at least pre-washed. In old days, wash was soaked, rubbed/scrubbed, rinsed, then put into soapy water to boil. This was done to mainly get rid of any remaining soils without harsh rubbing. Also boiling would release soap from textiles so the subsequent hot or warm rinses could carry it and any soils away.
Later, when sodium perborate came upon the scene, boiling was done to whiten and sanitise laundry.
The only time soiled linen is put into a boiling pot was when it was known to be infested with vermin (lice, bed bugs, fleas....), or was used by a person with an infectous disease. Think of Mammy asking for Mr. Kennedy's pants (that had lice) so she could put them into the "berling" pot.
That being said, if you want to boil laundry on a stove top find yourself a good deep stock pot. Fill partially with warm water, then add whatever detergent, soap and so forth you are going to use, then stir until dissloved. Add laundry then fill with more water to cover at least about 1 inch over the top of laundry.
Next simply turn on the fire and wait for things to happen. As the water heats it will expand and laundry will start to float up, you will need a long wooden spoon or something to act as a "laundry stick" to push things down and give them a stir.
*WARNING* If you are using oxygen bleach or a product containing same, as the water heats the hydrogen peroxide will start to release oxygen and foaming leading to "boiling over" of wash water. Keep an eye on things and lower flame accordingly.
Boiling really shouldn't take place longer than ten minutes, fifteen at the most, after that you run the risk of damaging the textile's fibers. If you are using the proper dosage of oxygen bleach and or detergent this amount of time is plenty.
Once finished boiling either use your laundry stick or a pair of tongs to transfer the wash (use caution, VERY hot) to a sink or another vessel to either rinse, or carry to washing machine if rinsing will take place there.
It is possible to simply carry the stock pot full of water and dump the lot in the sink, like when cooking pasta. However if the pot is heavy and water very hot, you are looking at an invitation for serious burns or injury.
After boiling best to rinse items at first in hot or at least warm water for the first few rinses. You want to bring down the temperature gradually to prevent shocking the fabric and causing creases.