Look, you need to try a literature search or at least a good textbook and then ask a real question. You appear to be at a University, I am sure you have a library that could assist you if you are unsure how to conduct a literature search or find a book. 

Please try harder.

This is (or rather was, we treat diseases now) a huge and old field, so I will give you some landmarks as guidance.

In anamniotic vertebrate embryos, like frogs and fish, the separation of the layers is morphologically and molecularly identifiable before gastrulation. In frogs, you can culture separately animal caps, marginal zone, and vegetal cells, they will yield epiderm, mesoderm (notochord and somites) and endoderm, poorly patterned but recognizable. Amniotes like chick, mouse and our humble selves start with one official layer, epiblast, which through gastrulation generates mesoderm and endoderm, while nongastrulating cells make ectoderm (note: endoderm is actually a mix of epiblast-derived cells with resident visceral endoderm, which is therefore not purely extraembryonic tissue as originally thought. This was recently shown by genetic tracing and spectacular imaging in mouse, but much older, and unquoted work in chick had seen that by manual labeling of hypoblast cells - VE equvialent in chick - decades ago). Read excellent chick work of Claudio Stern on what happens in the node and primitive streak during gastrulation, how endodermal and mesodermal cells are separated. Many of the experiments are cellular tracing - genetic or vital dyes -, plus molecular interference experiments that will shift the balance to one or the other of the layers (maternal-zygotic absence of EGF-CFC - crypto-like nodal coreceptor - in fish makes mesoderm only in the tail) but stem cell differentiation into embryoid bodies can also be directly observed in vivo, and it does work, more or less, in the 3 layer pattern. There are embryonic SC differentiation protocols which use a graded approach, starting with, say, endodermal commitment, then moving toward a specific fate. The neural crest is indeed a special type of cells, fairly recent in evolutionary terms, that is capable of moving from it's neural origin to other layers, which indicates natural plasticity in the layer commitment of a cell. In adult life, epithelial to mesenchymal transition, and its reverse MET, function in specific physiologic or pathologic (metastasis) conditions.

Hope this helps,

Alin

With regards to how this was established in the mouse, the following first reference which is a fate mapping study is one of the earlier studies performed in great detail in mammals. The article is now available free from Development. The second reference is a discussion of the results obtained in the original study.

Clonal analysis of epiblast fate during germ layer formation in the mouse embryo.

Lawson KA, Meneses JJ, Pedersen RA.

Development. 1991 Nov;113(3):891-911.

PMID: 1821858 - Free Article

Clonal analysis of cell fate during gastrulation and early neurulation in the mouse.

Lawson KA, Pedersen RA.

Ciba Found Symp. 1992;165:3-21; Discussion 21-6. Review.

PMID: 1516475

As mentioned, the earliest concepts of layers was derived mostly from observations.  Pretty astute observations though.  The sea urchin was particularly useful for this as the segregation into layers is quite early and obvious.  Once the concept of layers was established, everyone viewed their embryos through that lens and for the most part, the concept fit pretty well.  Now we have molecular markers that fit reasonably well with those observations and classic experiments that back most of it.  One example to start with is the the animal cap experiments of Nieuwkoop that demonstrated mesoderm induction.  Now that we have a molecular level of understanding the details, the mechanisms of segregation and specification of germ layers is considerably more complex and an ongoing issue in understanding how to efficiently differentiate stem cells.  The one exceptional cell type that complicates the three germ layers concept are the germ cells themselves.  A great start to reading up on this is the textbook of Scott Gilbert.  I believe that some earlier editions that are still relevant are available online at no cost.

Cheers, Tom