The default: airtight, opaque, cool, dry
For almost all tea, the goal is to slow change down. An opaque airtight container in a cupboard away from the hob covers it. A clear glass jar on a sunny worktop is close to the worst available option and is unfortunately the most attractive one. Keep tea away from spices, coffee and anything strongly scented — leaf absorbs aroma readily, which is the same property that makes jasmine scenting possible.
The exception: tea that is meant to keep changing
Sheng pu-erh, pressed white tea, some Liu Bao and traditionally roasted oolong are bought to age, and ageing needs a little airflow. Sealing them airtight stalls exactly the development they were bought for. Store these in their original wrappers in a stable, ventilated, odour-free space — not sealed, not in the fridge, and not next to anything aromatic. Stable conditions matter more than any particular temperature or humidity figure.
The refrigerator question
Refrigerating opened tea is generally a bad idea: it is humid, it is full of odours, and every time the container comes out, condensation forms on cold leaf. Sealed unopened Japanese green tea is the exception — it is commonly refrigerated or frozen, and matcha in particular dulls quickly at room temperature. If you do refrigerate, let the sealed container come fully to room temperature before opening it.
How long tea keeps
Green tea and lightly oxidised oolong are best within a year and noticeably duller after two. Black tea keeps two to three years without much loss. Roasted oolong improves for a year or two as the roast settles, then plateaus. Aged white and dark tea have no useful upper limit if stored well. None of this is a safety question — old tea is stale rather than unsafe — so the honest advice is to buy in quantities you will drink within a season.