The best way to keep clean is though prevention.
Install a "First Flush" diverter before water discharges into the tank. This will allow the first few minutes of water to flow past the tank and allow any debris to be washed away first.
Also try to have the tank out of sun light to eliminate the growth of algae, mold and scum. A black tank will work also.
To eliminate the growth of mosquitos the tank should be sealed to prevent bugs or organisms from laying eggs.
For more information:
Read "What is the healthiest option when choosing a rainwater tank?" a Q&A answered by Lee Hall.