If you are asking how it has been determined that the body is made up of a certain percentage of different elements (i.e. 60% oxygen, 18% carbon, etc.), it has been done using dead human specimens (cadavers) through dissection and chemical reactions. If researchers want to find the different amount of elements in each organ, they dissect out these organs separately. To determine the moisture content of the specimen(s), they dry them. Other chemical reactions are carried out to detect the presence of other specific elements -- for example: nitrogen content can be determined by the Kjeldahl-Wilfarth-Gunning method (which involves mercury as a catalyst), ash remaining in dessicated tissue specimens can be used to determine calcium content (using colorimetry) and phosphorus content (using colorimetry or the phosphomolybdate titrimetric procedure). I'm not expecting you to know these chemical reactions (I don't know them myself!), but it's just to give you an idea that different reactions are used to detect different elements in tissues. I hope this helped answer your question!

The only real way to get the atoms out of the body and study them individually is to take a sample of tissue and run it through a gas (really plasma) chromatograph, which ionizes the atoms and then shoots them through a magnetic field. The electric charges on the ions cause them to interact with the magnetic field and change direction, but the more massive they are, the more they resist the effects of the field. As a consequence, you can get the proportions of the different kinds of atoms based on what frequency the atoms strike different positions on your sensor after having been shot through the magnetic field.

As for the number of atoms total, once the masses and proportions of different elements are known, you can get the number of atoms per gram using Avogadro's number and thus the number of atoms in the body from the mass of the body.