To make hot chocolate from scratch is easy. 

Heat milk over low heat and then add shaved chocolate or cocoa and sugar to taste. 

To make the drink frothy, mix with a hand blender once chocolate has blended. 

Here's a basic recipe:

Heavenly Hot Chocolate

(Makes one cup)

Ingredients:

1 cup of milk

2 tablespoons granulated sugar

2 teaspoons unsweetened cocoa or shaved semi-sweet chocolate

A pinch of salt

¼tsp. vanilla  (for a variation, experiment with other extracts like peppermint or almond)

Directions: 

Mix sugar, cocoa or chocolate and salt in a mug.  Heat milk until hot on the stove or in the microwave for a minute and a half on high or until it is hot.  Be careful not to overheat.  Add milk to cocoa mixture in mug gradually until blended.  If using semi sweet chocolate keep stirring mixture so that the chocolate does not settle to the bottom.  If mixture is too sweet, adjust the amount of sugar to taste.

Options:

For mint-flavored hot chocolate, sprinkle with crushed peppermint and add a candy cane to stir.

Try spicing up your hot cocoa with ginger or nutmeg.  Start with about a ½ tsp. of each and adjust to taste. 

For a special twist, add a pinch of orange zest and stir.