There’s a messy job that is best done outdoors if possible.
You’ll need a new pot, somewhat larger than the older one. Despite internet lore telling you a pot needs to be only 1″ larger than the last one, any larger size will do. The concerns over a pot that is much larger are that the roots won’t reach through all of the soil to start so some soil may stay wet for longer than is healthy for the plant. So if you go to a much larger pot, you will have to careful watering the plant until the root system fills out.
Gently remove the plant from the old pot. If the plant is root bound you may need to slide a knife around the inside edge of the pot. If the soil is too wet it may fall off the plant taking a large chunk of the root system with it. So use extra caution if the soil is very wet.
I dump all the old soil into a trash bucket. Gently get as much off the old soil off the roots as you can with out damaging the roots. If you are repotting an orchid, same thing goes, you are just removing moss instead of dirt.
Then the messy part comes. I rinse in the sink the roots, the plant, and get it all cleaned up and have a good look at everything. Cut off any dead roots, leaves etc.
Put a few inches of soil in the bottom of the pot. If the pot is deeper than this plant needs add styrofoam peanuts or small rocks to the bottom of the pot to prevent the bottom soil from staying wet all the time. If the plant tends to be top heavy, like an orchid planted in moss use a few rocks to keep the plant from tipping over. Otherwise styrofoam will be lighter and make the pot lighter to move about for watering and maintenance.
Spread out the roots as much as you can with out doing damage. Place the plant in the pot with one hand, gently fill in with soil or moss with the other hand.
About the only time I fertilize my house plants is when I repot them. I use a liquid fertilizer with rooting hormone.