How are the elements differentiated? And how many protons occur in hydrogen, helium, and lithium?

The number of protons is the same as the atomic number (hydrogen is one, helium two, lithium three etc.) and the number of electrons is the same as the number of protons (assuming the atom is neutral.)

The more tricky bit is figuring out the number of neutrons. You do this by finding the mass number from the periodic table and subtracting the atomic number (the number of protons you found earlier.) Thus hydrogen has zero neutrons, helium has 2 (the mass 4, minus the no. of protons, 2), lithium has 4 (7 - 3) etc.

A quick check is to find the number of protons uranium-238 has. If you get the number 146, you've sussed it.

The periodic table gives an atomic number and weight for each element.

The atomic number is the number of protons in an atom of the element.

The atomic weight equals (very nearly) the number of protons plus the number of neutrons. Subtract the atomic number from the atomic weight and you'll be very close to the number of neutrons.
(but see the exception noted below)

The number of electrons will usually equal the number of protons. This is in a "normal", electrically neutral charged atom. Atoms often give up one or more electrons (or accept an additional one or more electrons), in which case they are "ions".

Atoms may also have more (or fewer) neutrons, in which case they are called "isotopes" of the element. "Deuterium", for example, is an isotope if hydrogen with an extra neutron. Chemically, these atoms behave the same as for the normal version of the element. Atomic number is the same, but atomic weight will be greater (or less) than the atomic weight given on the periodic table.

Whew. Haven't read up on this stuff for years. You now know everything I know on this subject.

And have you got a Table handy? Of course you have because you are doing your chemistry homework. #Z=1#, we gots hydrogen; #Z=2#, we gots helium; #Z=3#, we gots lithium;.....#Z=26#, we gots iron.

Now #Z# refers to the number of massive, positively charged particles that are present in the element's nucleus. And so for iron, #Z=26#, there are 26 nucular protons......but if there are 26 fundamental positive charges, to preserve electrical neutrality, the element must also be associated with 26 fundamental negative charges, and these are the electrons, which are conceived to whizz about the nuclear core.

The nucleus also contains massive, neutrally charged particles, i.e. #"neutrons"#. Neutrons (and protons) are conceived to participate in the strong nuclear force, which binds the nucleus together, and at short ranges is strong enuff to overcome electrostatic repulsion. Note that nuclei can lose or gain electrons to form positive or negative ions; they cannot lose or gain nuclear particles in a chemical process.

The nucleus of given element can contain various number of neutrons, and this gives rise to the phenomenon of isotopes. These are nuclei of the same element (because #Z# is the same), but their masses are slightly different, because of the presence of different numbers of neutrons....

I will give you one example of common isotopes. Hydrogen comprises (as far as we know) maybe 70% of the matter in the universe. Most hydrogen atoms contain only the one proton, i.e. we gots #""^1H#, #"the protium isotope"#; a few hydrogen nuclei contain one NEUTRON as well as the defining proton, i.e. we gots #""^2H#, #"the deuterium isotope"#; and fewer hydrogen nuclei contain TWO NEUTRONS as well as the defining proton, i.e. we gots #""^3H#, #"the tritium isotope"#.

Confused yet? Remember chemists and physicists are simple folk, and I don't think these concepts are entirely off the wall and inaccessible.

And see this old answer.