Green tea does not spoil, it fades. Kept badly it slowly loses aroma and flavor, and the difference is easy to miss because it happens gradually. Kept reasonably well it stays good for a long time, and there is not much to it.
Four things matter: air, light, heat and moisture. In that order.
Air
Oxygen is the main problem. That is why Japanese tea is vacuum packed or nitrogen flushed, and why an opened pack behaves differently from a sealed one.
An unopened vacuum pack keeps well for well over a year. Once you open it the leaf is in contact with air, so it is worth being a bit more deliberate: push the air out before you close it, or move the tea into a container that roughly matches the amount you have left.
There is no deadline. A pack you opened a few months ago is still perfectly good tea, it just will not have quite the aroma it had on day one.
Light
Sunlight breaks down the compounds that carry aroma. A clear glass jar on a sunny shelf looks lovely and does the tea no favors.
Keep it in something you cannot see through, somewhere out of direct light. That is the whole rule.
Heat
Warmth speeds everything up. Above a stove, next to a kettle or on a sunny windowsill are all bad. A cupboard on the other side of the kitchen is fine.
Moisture and smells
Dry leaf pulls in moisture and odor from whatever is around it. Do not store tea next to coffee, spices or anything with a strong smell, and do not measure it out with a wet spoon.
About the fridge
An unopened, vacuum sealed pack can go in the fridge or freezer and it will keep longer.
An opened one should not. Every time you take a cold pack out, condensation forms on the leaf, and moisture is exactly what you were trying to avoid. If you do refrigerate a sealed pack, let it come to room temperature before opening it.
What to keep it in
A container that seals, blocks light, and roughly matches the amount of tea you have. A canister with an inner lid gives you two barriers instead of one, which is why Japanese tea canisters are built that way.
Match the size to your pack. A 100 g bag in a 300 g canister leaves a lot of air sitting on top of the leaf.
Matcha fades faster
Ground leaf has far more surface area than whole leaf, so it changes quicker, and with matcha you can see it happening: a bright green powder slowly turns duller. Close the tin firmly after every use and keep it out of the light. An unopened tin can be refrigerated, with the same point about condensation.
Matcha that has gone dull or yellowish is past its best. It is still fine to use in a latte or in baking, where the milk and sugar carry it, but for whisking on its own you want it bright.