How do 2 chemicals react together to make another, like hydrochloric acid (HCl)?

When chemicals react with each other, chemical changes take place. In chemical reactions, the chemical composition of the reacting substances are different from those of the products. The chemical changes may also be accompanied by a generation of gases, a change in temperature or color, etc.

Two or more compounds can react with each other by breaking the existing bonds and forming new ones. There are two types of bonds: ionic and covalent. While the former is made between two species, one of which donates electrons and the other of which accepts, the latter is made between species that share electrons. 

For example, the following reaction yields hydrochloric acid:

H2 +Cl2 -> 2HCl

Here, the covalent bonds between the hydrogen atoms in the hydrogen molecule and those between chlorine atoms in the chlorine gas molecule are broken. These atoms then undergo ionic bonding to form the hydrochloric acid. 

Thus, the rearrangement of bonds or breaking and formation of bonds results in the formation of new products.

Hope this helps.