Testing frequency depends on how you use your pool, the weather, and the amount of traffic your swimming pool sees. It is better to check the water daily for new pools until you get used to your swimming habits, climate, and the other factors at play.
On average, you should test for:
Chlorine levels: 2-3 times a week
pH levels: Twice a week
Total alkalinity: Once a week
Calcium hardness: Once a month
Salt levels: Once a month (for saltwater pools)
Total dissolved solids: Once a month
Metals: Once every 3-4 months