For a strong acid, the equilibrium lies (strongly!) to the right. HX (X =Cl, Br, I), H_2SO_4, HClO_4 are all examples of such "strong" acids. You should practise writing the equilibrium with these strong acids.
Weak acids are those acids for which the equilibrium lies to the left, the reactant side. These include HF, H_3CO_2H, H_3PO_4, H_2S. Do not be intimidated by H_3O^+, it is simply a water molecule with another H^+ added (are mass and charge conserved; its formal name is the hydronium ion). In water, we conceive the acid species to be a cluster of water molecules (2 or 3 or 4 or 5) with an extra H^+ associated.
For the reaction above, the representation,
HA rightleftharpoons H^+ + A^-, is entirely equivalent and acceptable.
To measure H^+ or H_3O^+ we use the parameter pH, short for pouvoir hydrogene, which is -log_(10)[H^+].
