First separate into ions where appropriate following these rules.
1. If aq write ions if strong electrolyte; as molecule if not.
2. Write as molecule if gas
3. Write as molecule if pure liquid
4. Write as molecule if solid.
2H^+(aq) + 2Br^-(aq) + Ba^2+(aq) + 2OH^-(aq) ==> 2H2O(l) + Ba^2+(aq) + 2Br^-(aq)
Now to turn the complete ionic equation into the net ionic equation just cancel the ions common to each side. The net ionic equation is what is left.
I see Br^- on both sides. I see Ba^2+ on both sides. Cancel those on both sides. That leaves you with
2H^+(aq) + 2OH^-(aq) ==> 2H2O(l)