Short Answer:
The best approach combines physical removal, aeration, and nutrient control, with chemicals as a last resort.

Detailed Answer:
Step-by-step strategy:

Remove algae manually (rake or skimmer)
Install aeration to reduce nutrient availability
Use beneficial bacteria to break down organic waste
Bind phosphorus (products like Phoslock, MetaFloc)
Use algaecides only when necessary

Important:
Algaecides kill algae but do not fix the root cause—nutrients.