A hydrogen atom has one electron. The hydrogen atom is simply made up of one electron and one proton that are bound together by an electromagnetic force.
In order for a hydrogen atom to exist, it must have both an electron and a proton. The electron has a negative charge and the proton has a positive charge, and these charges work against each other to make the electromagnetic force that holds the entire atom together. They are constantly working against each other because one is positive and one is negative, but their repulsion is what makes the hydrogen atom exist. Occasionally, the electron will escape from the proton and the hydrogen will then become a positively charged ion. The hydrogen atom is capable of locating a new electron when this happens.
In the past, it was not uncommon for hydrogen atoms to be shown as a very large proton with a very small electron sitting on the edge of the atom. While this was easy for people to visualize, it was not an accurate representation. The proton is much stronger than the electron, but it is not necessarily bigger than it. The electron is now shown as a force that encapsulates the entire atom and makes up the majority of the atom, instead of being a simple speck sitting on the edge of the atom.