Here are some recommendations:
Remove soot as much as possible first by shaking it off outdoors, run water over the clothing wrong side out, so the water flushes the soot out of the clothing, pre-treat w/ laundry stain remover,
then launder your clothing.
This is a recommendation from Tide:
Wash your hoodie in Lestoil. It is recommended for mechanics and other people who get their clothing very dirty and greasy.
Persil is a good brand for this issue with soot, smoke stains, and smell removal - www.persil.com/
First gently shake out of clothing any excess soot.
Then wash as recommended on the care label using heavy-duty detergent (Persil or Tide), follow the directions on the packaging. Use the temperature recommended on the label.
Check if stains are removed before drying. If stains remain, repeat the washing.
Hopefully you have had success with one of the suggestion.
It's always a good idea to also post what type of material the stained item happens to be as this gives us a better idea of what type of product may work best.
If your hoodie is all cotton you should be able to remove soot or other stains with just a few extra steps.
Shake off/dust off any loose soot first.
Rinse with clear water and add any one of your regular laundry detergent or Dawn dish soap to the spot and let soak for 5-20 minutes.
Wash in regular medium hot - hot water and check to see if stain is gone. let it dry naturally just to make sure the stain is gone.
Launder again and dry if all stains are gone.
Some people use white vinegar/water soak and sometimes it works. Mix three parts warm water to one part vinegar.
Also, baking soda can be used:
1 cup baking soda to water to cover garment. Mix and place garment to soak for 30 minutes.
Wash as usual.
If it is cotton or a cotton blend (usually nothing works well on 100% poly or rayon) you can try mixing 2 cups COLD water, 1 cup hydrogen peroxide, one cup baking soda in a large bucket. Add a big dash of a blue dawn liquid dish soap and swish it all around, then let the jacket soak (stain side to the liquid) in it for 15 minutes. Remove, rinse in cold water and re-soak if the stain is not completely out.
If it is is not out by the second time, you can try mixing that same combination with Dawn AND a regular Tide liquid (a tablespoon) and let it soak again.
Do not use hot water as it will set the stain. Do not dry in the dryer until the stain is completely gone.
Sometimes drying it in the sun will help lighten it.
Once the stain is gone, wash normally.
Soot can be deposited on walls from smoke or even a poorly trimmed candle wick. This is a page about removing soot from walls.
Sometimes candles can burn quite sooty. The black soot sticks to the inside of the candle jar, looking unattractive. This page contains ideas for removing soot from candle jars.
This is a page about cleaning soot from bricks. Soot on your fireplace bricks can be unsightly. In addition to a number of spray cleaners that can help remove the stains, you may find that a soot sponge does the job too.
Bon Ami can be a great cleaning an polishing agent, even on tough stains like soot. This is a page about bon ami polishing paste to remove soot.
Soot can collect on the door glass of your wood stove. This page contains several suggestions for removing black soot from a wood stove window.
This page is about removing soot from curtains. Soot residue can collect on fabric from wood burning and candles.
This page is about removing soot from wood furniture. Any house fire can leave you with usable wood furniture if you can remove the soot.
This page is about removing soot from carpet. Even a small house fire can leave you with a dirty carpet.