According to the planetary model, an atom consists of a positively charged nucleus and negatively charged electrons orbiting around the nucleus, similarly to the planets in the solar system orbiting around the Sun.
The nucleus is composed of positively charged protons and neutral (not electrically charged) neutrons. The size and mass of a proton and a neutron is approximately the same. Protons and neutrons consist of elementary particles called quarks. The quarks carry fractional electric charged and are bound together by force called "strong nuclear" force.
The radius of the nucleus is much smaller than the distance between the nucleus and the electrons, and thus the radius of the whole atom. The radius of nucleus is typically measured in femtometers, or `10^(-15)` of a meter. The radius of an atom is measured in angstroms, or `10^(-10)` of a meter. So, the radius of a nucleus is approximately 10,000 times smaller than the radius of the whole atom. (When you see a picture of an atom as a round nucleus with a few electrons orbiting around, keep in mind that it is not drawn to scale!)
The atom can contain as few as one electron (such as in the Hydrogen atom), or many more. However, the number of protons in the nucleus is always the same as the number of electrons, because they carry electric charge that is equal in magnitude but opposite in sign, and the whole atom is electrically neutral.
While planetary model of an atom explains some properties of atoms and molecules very well, it is not entirely correct. According to the theory of electromagnetism, an electron cannot actually orbit around the nucleus indefinitely, because it would then emit electromagnetic radiation, which means it would lose energy and eventually fall onto the nucleus. The theory of quantum mechanics resolves this contradiction by describing electrons as waves which are only allowed to have specific frequencies and wavelengths, corresponding to the possible orbit paths the electrons can follow.