Weak Acids
Weak acids, like weak bases, are equilibrium mixtures, consisting of a higher concentration of reactant molecules than product ions.    A weak acid like acetic acid is written as:
                     H2O + CH3COOH   <------->  C2H3O2- + H3O-
                                                the acid hydrogen
The H at the start of the formula is termed the acid hydrogen since it is this H atom which reacts with the water to form the acidic properties of the solution. You know it as the H on the -COOH portion of the carboxylic acid in organic acids.
In solution, weak acids have a very low degree of dissociation. eg. a 0.10 mol/L solution of HCl is 100% dissociated, whereas a 0.10 mol/L solution of acetic acid is only about 1.3% dissociated.
eg.                            HCl      +     H2O -----> H3O+    +    Cl-
              before    0.10 M                                 0 M          0 M

                after         0 M                              0.1 M         0.1 M

For acetic acid we need some equations:
                      CH3COOH + H2O <------->  H3O+ + CH3COO-
You can see from the equation that the moles of acetic acid dissociated = the moles of H3O+ formed which is also equal to the moles of CH3COO- formed.
Since only 1.3% of the 0.10 mol/L dissociate then the [] of each ion is:
1.3% * 0.10 mol CH3COOH = 0.0013 mol H3O+= 0.0013 mol CH3COO-
100              1 L solvent                       1 L                                   1 L
Follow-Up Problem
A 0.60 mol/L solution of formic acid, HCHO2, is 1.8% dissociated. Calculate the [] of each species (excluding the water) in the equilibrium system