How do scientists make fate maps?
By tracking cells of the embryo to look at where they go as development progresses.
In its simplest form, it is possible to inject a single cell of the embryo at an early stage (the 8-cell stage, for example) with a vital dye such as methylene blue or even India ink. All cells that arise from the thus marked cell will carry the dye. This technique has the obvious drawback of 'dilution' of the dye with each cell division, and is therefore not feasible for long term tracking. Other methods like radioactive and fluorescent labeling also have the same drawback.
Chimeric embryos can be generated to create fate maps. For example, a graft of cells between two very similar species (eg chick and quail) will not be rejected and downstream cells can be probed for their species of origin.
Gene editing tools (eg Cre-Lox) can also be used. For example, the gene for Green Fluorescent Protein (GFP) can be incorporated into a cell, and all daughter cells that arise from this cell can be tracked easily by fluorescence microscopy.