Now the basic compound has been back-extracted into the dichloromethane* layer.

Water and inorganic compounds form a distinct layer, which is easy to separate. A small amount of water and inorganic compounds are dissolved in the organic layer as well.

Drain the bottom (dichloromethane) layer into a clean flask to separate from the aqueous layer.

(Tip: one more back extraction with another 1/2 volume of fresh dichloromethane will ensure that most of an organic compound is extracted from the aqueous layer. In such a case, you will continue with the combined dichloromethane extracts.)

Your compound is dissolved in the dichloromethane phase. How will you isolate your compound from the solution?

Filtration
Distillation
Recrystallization