Carefully remove some, but not all of the soil ball from around the roots, being careful not to damage any of the roots. To re-pot, the plant and the top of the soil ball should be slightly below the lip of the pot. Add potting mix to fill the bottom and around the sides of the soil ball. Gently tap the pot or poke gently around the edges to settle the soil in around the roots. Water thoroughly. If the new soil mix settles too much along the edge of the pot, add more soil to bring it level with the top of the root ball.

The mold growth you refer to may not be mold, but rather accumulated mineral salts from our softened water or from fertilizer residue. Those can be repotted as well making sure to remove most of the old soil so as to remove the buildup of the salts.

If indeed the residue you see is mold, the plant is being overwatered, or the potting soil may be too compacted and holding moisture too long which would call for repotting as well. In either case of salts or mold, make sure containers are thoroughly cleaned with a 1:10 bleach solution before using.

Here are some helpful links for repotting houseplants: 

https://www.uaex.edu/yard-garden/home-landscape/docs/Repotting%20Houseplants.pdf

http://www.ext.colostate.edu/ptlk/1316.html

http://www.ext.colostate.edu/ptlk/1318.html