A few "element"ary questions.?

Can someone please tell me "how did we discover the different elements". . . . . . , and exactly . . . . . "how did we find out how many protons, neutrons, and electrons they have?"
How do we even know what they look like?"
With magnafying glasses?

Answer:
This isn't an easy question to answer, as there are many parts, but I'll try to make it as concise as I can.

"how did we discover the different elements"

Long before any experiments were conducted, the Greeks theorized that all matter was either composed of or could be classified by four specific "elements": earth, fire, water, and air. That theory held well in the community for about 2000 years, until the branch of alchemy (the attempt to create precious metals like gold from cheaper ones) emerged and began to dissolve this theory. It was during this time that some of the "metallic" elements (gold, silver, and copper, for example - though I'm not entirely sure) were recognized - not necessarily "discovered", per se, as they had already been in common use.

Throughout the 1600s and 1700s, chemistry became the prominent branch of science, specifically with the discovery of gases such as nitrogen, carbon dioxide, hydrogen, and oxygen.
Over time, these chemists began to organize these elements based on mass (the organization led to the development of the periodic table), and thus scientists (the most notable being Dmitri Mendeleev) were able to predict the masses of missing elements. By the mid-late 1800s (I'm not exact on this time period), mass spectroscopy - a process that allows scientists to determine the relative masses of elements - was in widespread scientific use as well. Put the prediction of masses together with mass spectroscopy, and you, just as other scientists did, discovered other possible elements.

Fast forward to today, where particle accelerators and other technology bombard protons of various isotopes to (albeit briefly) attempt to synthesize new elements (the ones past 112, I believe, commonly referred to as "superheavy" elements).

So, in short, alchemy and early experimentation revealed the most common metallic and gaseous elements; the periodic table, mass spectroscopy, and particle accelerators handle the rest.

"how did we find out how many protons, neutrons, and electrons they have?"

This question can be answered by the periodic table, though a great deal of discovery here was based more on assumption than on actual experimentation. Mendeleev's earlier table was arranged by atomic mass, yet was accurate enough that he could predict the masses of missing elements by examining such "gaps" between two (possibly more) elements. One example was indium (In), an element that had been discovered but not yet "defined". In was assigned an atomic mass of 76, based on Mendeleev's assumption that indium oxide had the formula InO. He discovered it was incorrect, however (the real formula is In(2)O(3)), and adjusted the mass so that it was instead assigned to 113 (the mass it holds today).

But how does this determine protons and neutrons? Two reasons: (1)Mendeleev's reorganization of the table, and (2)the definition of mass number.

(1)Mendeleev's table of masses had its flaws. For example, cobalt and nickel were originally defined such that nickel preceded cobalt in terms of mass. But later proof (sorry, I'm not exactly sure how this was proved - other sources can help) determined that nickel had more protons than cobalt (nickel has 28, cobalt has 27). It was a minor flaw (at least, one example of one), but such flaws were enough for Mendeleev to arrange his table based on increasing atomic numbers (i.e. numbers of protons). This is the current format used today.

(2)Once Mendeleev reorganized his table based on protons, it was now easy to calculate neutrons (even easier for electrons). Mass number (an integer form of atomic mass) is defined as

Mass # = # of protons + # of neutrons

For missing elements, all Mendeleeev had to do was predict their masses (this still worked even after reorganization), determine their atomic numbers, and solve for the number of neutrons. Finding the number of electrons was even easier; all elements have a natural tendency to remain neutrally charged - that is, their positive (+) and negative (-) charges balance. Therefore, it makes sense that a neutral atom would have the same number of negative charges (electrons) as positive charges (protons). As such, the number of electrons in any atom of an element is equal to the number of protons of that element.

"How do we even know what they look like?"

This question is resolved through the use of scanning electron microscopes and tunneling electron microscopes (SEM and TEM, I think that's what they're called). Unfortunately, I know very little about how they work, so you'll have to find another source for this info. However, they are able to display high-resolution, high-quality images of even the smallest sample of atoms.

I hope you were patient enough to read this monster of an explanation.
Big question whole books written on this topic. Atoms are way, way smaller than you can see in a magnifying glass.

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