This page is intended to be a brief introduction to the general concepts of chemistry. It does not go into any deep detail, nor does it talk much about specific chemicals, what you can do with them, or how you mix them. As such, it may not be terribly interesting to people who just want to mix things together, but for people who actually want to study and understand chemistry, an understanding of boring general concepts is unfortunately necessary before you can start engineering your own chemicals.
Let's start by covering the smallest category of matter currently known to mankind: Particles. In most mainstream chemistry, there are three types of important particles: Protons, neutrons, and electrons. There are several other types of particles including photons, muons, and kaons; However, although much new research is being done regarding them, these particles are still not well understood, and so most of today's chemistry theory stems from understanding the three classic particle types.
Protons have a positive electrical charge. They are found in all atoms; The number of protons in the atom is the atomic number of the atom.
Neutrons exist in most, but not all, atoms. Unlike the other two main types of particles, they do not have an electrical charge. Like protons, neutrons are found at the nucleus of the atom. Neutrons have slightly more mass than protons.
Electrons have a negative electrical charge. Unlike protons and neutrons, which form a compact nucleus at the center of the atom, electrons instead orbit the atom; They circle around the nucleus in a never-ending orbit. Electrons are much smaller than protons and neutrons; They have a considerably lower mass.
Particles, by themselves, are quite simple. (At least as far as we understand them so far.) To form useful materials, particles are grouped together into atoms. Atoms form the fundamental building blocks of most modern chemistry; Little chemistry work is done at the particle level. Rather, most chemistry is concerned with the structure of atoms, so it is important to understand the composition of them.
An atom has two important sections: The nucleus and the electron cloud. The nucleus is the center of the atom, where a compact gathering of protons and (usually) neutrons exists. The electron cloud is a halo of electrons that orbit the nucleus. If you consider the overall volume of an atom, most of it is empty space; The nucleus is very dense, but outside of the nucleus is nothing but emptiness until you reach the electrons.
Because the nucleus only contains protons and neutrons (and recall that protons have a positive charge while neutrons have no charge), the nucleus itself has a positive charge. The atom's overall electrical charge is balanced out by the negatively-charged electrons around it. An atom with an equal number of protons and electrons has a neutral electrical charge. An atom with differing numbers of protons and electrons is not electrically neutral, and is usually called an ion. There are two types of ions: Anions and cations. An anion is an ion with a negative charge (that is, an atom with more electrons than protons). A cation is an ion with a positive charge (that is, an atom with more protons than electrons).
Now that you know the basic structure of an atom, it's time to learn about elements. Elements are chemicals which cannot be simplified or broken into smaller pieces without changing their basic chemical behaviour. Everything that we see in the world is made of elements, and what's amazing is how few elements exist. There are actually only slightly over 100 known elements, and the vast majority of them do not exist around us much in everyday life. There are only a few elements that occur commonly in nature and the typical human environment. Some of the most common elements are nitrogen (which is believed to constitute about four-fifths of the volume of the Earth's atmosphere), carbon (which charcoal is a form of), oxygen (which, as you probably know, is the stuff that our bodies need in the air we breathe), and hydrogen. Hydrogen is the simplest element of all: A hydrogen atom is simply one proton with one electron orbiting around it. Other elements get more complicated, but in general, an atom can be mostly defined by simply how many protons, neutrons, and electrons it has.
An element is defined by how many protons its atoms have. As just mentioned, hydrogen has one proton. That means that for something to be hydrogen, its atoms must have exactly one proton; If there is a different number of protons in the atoms, the chemical is not hydrogen. The number of protons a chemical has is called its atomic number. Generally speaking, the number of neutrons in an atom does not make that much difference to the chemistry of basic elements, but the number of protons is crucial, because from the number of protons you can tell exactly what element the atom makes.
If you want to start doing chemistry with specific chemicals, you should get a copy of the periodic table of elements, which is a table that specifically lists every known element by atomic number. Atomic number 1 is hydrogen, number 2 is helium, number 3 is lithium, and so on. It is beyond the scope of this general introduction to chemistry to list all the known elements, but the periodic table is readily available in all kinds of references, since it is a very important reference for virtually all chemists.
Where the number of neutrons in an atom does start to make a difference is when you start considering isotopes. Because an element is defined by its number of protons, it is possible to have two atoms which are the same element, but which have somewhat different chemical properties because of how many neutrons they have. Because neutrons have mass, an atom with more neutrons will be heavier than one with less neutrons, even though both atoms may be the same element. In this case, the two different types of atoms are said to be different isotopes of the same element. A relatively common example is carbon-12 and carbon-14. Carbon atoms have six protons (if they didn't, they wouldn't be carbon, of course) but carbon-12 has six neutrons, while carbon-14 has eight neutrons. These are two different isotopes of the same element. The isotope number, as you may have guessed, is simply the number of protons plus the number of neutrons. If you want to know how many neutrons a particular isotope has, just take the number of protons (which you can look up in the periodic table) and subtract it from the isotope number; The result is the number of neutrons. In the example of carbon-14, subtract the number of protons (which is six, because carbon is atomic number six) from the isotope number of 14. 14 - 6 = 8, meaning carbon-14 has eight neutrons.
Although all matter can be simplified into elements (as far as we know, anyway), obviously there are several thousand different chemicals that exist in our world. These are made by mixing different elements together. When you make a chemical that's a mixture of several elements, the result is called a compound. Compounds cannot be split into atoms without changing their chemical nature; Instead, the fundamental unit of a compound is the molecule.
A molecule is simply a collection of atoms grouped together. Molecules are usually expressed in terms of what atomic elements they have, and how many atoms of each element. Perhaps the best-known compound symbol in the world is that of water, which is simply two hydrogen atoms and one oxygen atom united into a single unit. The resulting unit is a water molecule, with a chemical symbol of H2O. This formula signifies that there are two hydrogen atoms (hydrogen's chemical symbol is H), and one oxygen atom (oxygen's chemical symbol is O). Note that the number 2 should be rendered in a subscript font (meaning it should be made small and dropped slightly below the H and the O), but since there is no way to do so if you are viewing this as a plain ASCII text file, I have rendered it as it is.
A slightly simpler chemical symbol is O2, which is a molecule containing two atoms of oxygen bound to each other. This molecule is somewhat confusing, because it is often also called "oxygen", even though oxygen is, properly speaking, the element, and O2 is actually two oxygen atoms together. (Many scientists, and also doctors and nurses in hospitals, usually say "Oh two" when speaking of O2, to avoid confusion with pure elemental oxygen.) O2 is the kind of oxygen that we breathe in the air; Elemental oxygen does not occur often in nature. O3 is another molecule made of oxygen atoms; It is simply three of them made into a molecule. However, O3, which is ozone, is poisonous to breathe, although it is the same ozone that constitutes the Earth's famous depleting "ozone layer" that blocks the sun's ultraviolet radiation. So we see that even though O2 and O3 are made of the same element, they have very different chemical effects: One is needed for human life, the other is poisonous to human life.
This concludes the main knowledge of basic atomic theory. The field of chemistry certainly gets much more complicated than this, but what you've read here should at least get you through most of high school chemistry, at least until the last couple of grades.