Growing crops works a bit different from vanilla Minecraft. There are a plethora of crops available for farming, which can be acquired by finding them in the wild. All crops are harvested by destroying the plant. Once harvested, the crop along with its seed will drop. The amount of seeds dropped depends on your agriculture skill.
Growing crops requires you to merely right-click the seeds on to a block of tilled soil, created using a hoe. If there is access to water, crops will grow faster. While it grows, nutrients from the soil will be depleted. There are 3 nutrients, and different plants consume them differently, allowing you to rotate the crops to optimize grow time. Planting the same crop again on the same farm-plot will cause the plant to grow much slower the second time. Note: tilled soil in TFC does not break when walked on.
Grains require a knife next to it in the crafting box, to remove straw. The straw will appear in your inventory when you remove the grains from the output box. Grains can then be milled at a quern to produce flour, which can be used to make bread.
When temperature drops below 0 (which can be seen using the F3-interface), there is a chance that crops will despawn and leave only a bag of seeds behind. The chance increases with every day of sub-zero temperature. The seeds will not despawn, as they appear the same way as rock- or stick-items on the ground. This happens both for wild crops as well as planted crops.
Throughout the world, you'll come accross fruit trees. These look different from normal trees, often not more than 4 blocks high, and the trunk not thicker than normal fences. Right clicking on leaves with fruit will harvest the fruit from that block. To get saplings, you must break the branches of the fruit tree, new branches will then grow out slowly. When a sapling is planted, it will resemble a lone fence post, give it time, and fruit bearing leaves will form and grow bigger as the months pass.
Additionally, you'll likely come across bushes with berries. Some bushes are flat, like carpets, others resemble blocks of leaves on the ground. Berries count as fruit in TFC, and are a good source of food early on. Bushes can be broken and replanted, but no new bushes will can be made, so take care of the bushes you have! Harvesting works the same way as with fruit trees, just right-click fruit-bearing bush-blocks. Watch out, some bushes are thorny, and will hurt you if you touch them.