To make detergent for delicate clothing, all that is needed are a few items that can be found at your local grocery store or online: a bar of gentle and mild soap such as Ivory, washing soda -- do not substitute with baking soda -- a large container and water if you want liquid detergent.
For liquid delicate detergent, grate the bar of soap and add to a quart of water in a pan and cook until it is dissolved. Put 4 gallons of hot water into the container, add a cup of washing soda and mix. Add the soap and water mixture and let sit overnight. Use about a half to a full cup of the mixture in either the washing machine or with hand washables.
For powder detergent for delicate clothing, grate the bar soap and mix with a cup washing soda in large container. Stir mix together and use as you would store-bought detergent.