To feed tame dinos in Ark Survival evolved, you can put the proper food in their inventory or place food in a feeding trough. The feeding trough can be crafted in your inventory from common resources (120 wood, 60 thatch, 40 fiber, 8 metal) at level 18. Place the feeding trough on the ground, or a foundation, load it with food and it will feed all the dinos within a circular area that extends about ten foundation widths from the trough. You will know if your dinos are within feeding range of the trough by a little trough icon that appears above the name of the tame while looking at it. This only means they are within range, not that they are eating. A completely empty trough with still show the indicator over the name.
One important thing to know about the feeding trough regards fish eaters. Some creatures like the otter, baryonyx, and ichthyornis only eat raw or cooked fish meat. Other carnivores will eat all kinds of meat, but they will eat fish meat before anything else. Unfortunately, that means your supply of fish meat will run out quickly, and your fish-eaters may starve. If you only have one or two fish-eaters, you might want to just put fish meat in the animals' inventory. One other note is to keep track of dinos with odd food requirements, you don't want your titanboas, sinomocrops or other weirdos starving to death because you forgot to feed them with eggs and chitin.
On single-player feeding troughs don't run out of food very quickly, but on a server they can run out pretty quickly, if you have a lot of dinos, plus food spoilage. Be sure to check on, and top them off often.