KoA has 4 types of resources: Food, Wood, Iron Ore and Silver. You can get these in 'raw' form, and as items.
'Raw' resources you get from harvesting your farms (food), sawmills (wood), iron mines (iron ore) and silver mines (silver) in your own city, or by sending your troops to those on the Kingdom map to gather, or from your Wishing Well.
They are also occasionally collected from system / alliance mails, and can be traded on the marketplace. At the top of your screen on the Kingdom map and Stronghold view you can see how much of these 'raw' resources you currently have in your Storehouse.
These resources can be stolen when you get pillaged by enemy players though. Resources under a certain limit might be safe in your storehouse, so it's a good idea to upgrade it as soon as possible. You can click on the 'Info' button of your storehouse to see how much is protected. The left number is the base protection limit, the green number on the right is the bonus amount from heroes and such. The total is what's kept safe should you be raided.
However, my advice is to spend it as soon as you can, and send up to your daily limit to our Alliance Storehouse for storage, to not be an appealing target for other high level players/alliances who like to 'farm' other, weaker, players for resources instead of gathering them themselves. Don't forget that you can donate to Alliance Tech if you've run out of things to spend on. ;-)
Resources also come in the form of items. As items currently can't be stolen, this is a much safer way of saving up resources for big upgrades. While you can use these items from your regular items interface:
It's much easier though to just click on the resource type at the top of your screen to open up the resources interface, as you can easily see how much you have here, and use the different types:
Since these resource items can't be stolen, try to only use them for big expenses, or when you really need a little bit extra for something. Otherwise it's imho often better to just wait a little while you gather some more, or use your wishes from your wishing well. It might take a bit longer, but at least you don't need to worry as much about losing resources when being attacked. Since you have less resources showing in Scout reports, it should hopefully also make you a much less appealing target.
Don't I need food to keep my troops alive?
No, you don't
If you click on the building at your Parade Ground, at the bottom left of your Stronghold view where your troops reside, you'll get an overview of all your troops (and the ability to save Troop Formations) with an info block that explains that your troops won't die when you run out of food:
Actually, your resources will never drop below the Storehouse limits, unless you spend them yourselves, and even then it's not a big deal if you hit 0. Your Upkeep cost will only apply on the resources you keep above the storehouse limits.