What is the chemical composition of the grignard reagent?
A Grignard reagent is an organomagnesium halide of the generic form $\ce{RMgX}$, where $\ce{R}$ is a hydrocarbon group and $\ce{X}$ is a halide, usually $\ce{Cl}$, $\ce{Br}$, or $\ce{I}$.

These reagents are produced by the reaction of magnesium metal with the corresponding organic halide in a non-protic (but coordinating) solvent, like diethyl ether. 

For example, you would make phenylmagnesium bromide from bromobenzene and magnesium:

$$\ce{PhBr(C6H5Br) + Mg -&gt;[][\ce{Et2O}]PhMgBr}$$

They are moisture and air sensitive, but not so much that you need to get crazy with inert atmosphere. These reagents are not stable outside of solution. 

Grignard reagents can be made in most laboratories set up for organic chemistry. In fact, they are very common reactions to include in undergraduate organic chemistry lab courses because they are very well behaved.