Matter is anything that has mass and takes up space. We are matter, your computer mouse is matter, etc. Matter is composed of molecules. Molecules are composed of atoms.
The basic atom is the hydrogen atom. It is configured much like a planet orbiting the sun. There is a nucleus which we can compare to the sun; and an electron, which we can compare to the earth.
It is important that our hydrogen atom is neutrally charged electrically. We know that hydrogen has a single electron, and electrons are negatively charged. In order for our atom to have a neutral charge, there must be a positive substance to neutralize the negative charge of the electron. Therefore; due to this theory, our atom must have a positively charged particle. This is called a proton. One positive particle and one negative particle cancel each other out, so our hydrogen atom is happily, neutrally charged. There is also another particle in the atom called a neutron, which is the same as the number of protons; but, we will not concern ourselves with neutrons. There are also sub-atomic particles that compose neutrons and protons; but, we will not concern ourselves with quarks, etc., either.
The distance between the electron and nucleus is huge in proportion to the size of the atom, which is not visible because it is so small. This distance between the electron and nucleus would leave a tremendous hole in everything if the electron was stationary. Our electron orbits the nucleus rapidly, taking up this space. This is quantum mechanics which concerns itself with an electrons position at a given space and time; but, we will not worry about that.
So, we have an electron that rapidly rotates around the nucleus. This is mass and takes up space, so this is matter. This is one atom of hydrogen. Each element, such as hydrogen, has a different number of electrons and protons which gives them specific properties and makes them certain elements, such as oxygen. Our hydrogen atom is the only atom that has one electron and one proton. This is the specific property of hydrogen.
In some cases, you can have one or more protons than electrons. This would give your atom an electrical charge which is positive. You can also have an atom with more electrons than protons. This will give your atom an electrical charge which is negative. An atom that has a positive or negative charge is called an ion. Either cations or anions, respectively.
Hydrogen is the most simple of all atoms, with one electron and one proton. As we go up on the periodic table of the elements, our other elements (hydrogen is an element), become more complicated because they have more electrons. If our element has a number of electrons that is greater than two, the electrons over the number two will have a higher orbit, or an orbit further from the nucleus. The first orbital area is only allowed two electrons. One spins clockwise, the other counterclockwise. The next orbital layer of electrons will hold eight. This layer of eight electrons is further out than the orbit of two electrons, and thus, is further away from the nucleus. Do not concern yourself with this. To simply understand how an atom works, we just look at the hydrogen atom.
As stated before, there is a nucleus, and one electron that orbits this nucleus. Since we have a neutral charge, because we have a hydrogen atom, not an ion, we will have the one electron and one proton inside the nucleus. We will also have one neutron. Just for general information, hydrogen is lighter than air. Hydrogen floats, and it floats because the components of air are heavier than hydrogen. Air is composed of molecules of different elements attached together by "bonds". This gives air many more electrons and protons and since these atomic particles are matter, the air mass is heavier than the hydrogen mass. I hope this simplifies the workings of the atom for you.