An example of homogeneous catalysis is esterification. An alcohol (eg ethanol) reacts with a carboxylic acid (eg propanoic acid) to form an ester (eg. ethyl propanoate) and water. The reaction is conducted under reflux (so temperatures in excess of 200C) and with a concentrated sulphuric acid (H2SO4) catalyst. It's homogeneous because the sulphuric acid catalyst is liquid/aqueous, just like the alcohol and carboxylic acid.
Another example of homogeneous catalysis is in dehydration/elimination reactions. An alcohol (eg. ethanol) is reacted with a concentrated phosphoric acid (H3PO4) or sulphuric acid catalyst to form ethene and water. If a more complicated alcohol such as propan-2-ol is used, multiple isomers of propene will form.