The #HCl# molecule is formed between a neutral hydrogen atom and a neutral chlorine atom.
Hydrogen has 1 electron in its 1s-orbital, but it needs 1 more to form a stable configuration and complete its 1s-orbital (essentially reaching the configuration of #He#). Chlorine, being in group 17, has 7 electrons in its outermost shell, and needs one more to form a stable octet.
A covalent bond thus forms between #H# and #Cl#, each receiving the extra electron it needed (for more on #HCl#'s covalent bond read about electronegativity).
Now, since #HCl# is a strong acid, it dissociates completely in aqueous solution into #H^(+)#(which form #H_3O^(+)#) and #Cl^(-)# ions as a result of its reaction with water, which acts as a base.
Any further reactions between #HCl# and say, s strong base, will take place between the molecules' ions, like this: