Answer:

There are many theories on how best to do this. But most will advise to balance the pH and alkalinity and then add enough chlorine to shock the pool. You may also want to add an algaecide so that you do not have to add as much chlorine and to make the process faster. The algae will then die and drop out of solution. The filter should then take care of most of this, just make sure you clean and/or backwash your filter after clean up is done so the algae does not come back to life in your filter. Any leftover debris/sediment from the outbreak can be vacuumed up (before you clean the filter).