First of all, if you register a Kabam account yet you'll receive 80,000 food, 80,000 wood, 80,000 stone and 80,000 metals. This is a HUGE boost if you want to get a nice head start, especially if you have already unlocked some advanced troops
Keep your Storage Vault upgraded in order to hide resources from other players, and make them immune to getting stolen. This should be one of the first things that you use a Completion Scroll on, since it's so important. With a fully-leveled vault, you'll be able to set your troops on evade at all times because it won't be all that important to defend what few resources you have past 500,000 apiece. Most basically, upgrade your resource buildings. Build and upgrade farms for food, lumbermills for wood, quarries for stone and mines for metal. Upgrade your Fortress in the city view to unlock more spaces for resource buildings, too. Your goal here is to increase your hourly income, especially for food since that's already needed for upkeep of your troops.
The Grodz campaign can also make it much easier to earn resources, especially once you beat them all and unlock the Dragon in battle. But even early on in the Grodz campaign, send over large numbers of porters so that you can steal large amounts of resources from the Grodz bases. Send the Porters and (later on) the Armored Transports over to the other bases and camps that you attack as well.
You can buy more resources using in the store, but remember that you only get limited amounts of rubies. Complete quests in order to get fast resources as rewards. Hit the “collect” button in the quests menu on your completed quests, and the resources will go to your stockpile. Protect your resources by building and upgrading your warehouse.
Even if you already have the maximum amount of wilds in your possession, attack other wilds anyways whenever you need to refill one of your resources other than food. Anthropus Camps usually contain massive amounts of food, fairly large quantities of wood and miniscule amounts of stone and metals, so attacking hills and mountains is your best bet.