To begin farming you will need a few items. First you will need a ground tiller, this is a crafted item. To craft a ground tiller u need: 1 Pipe, 1 Wood Stick, and 4 Metal Shards. A ground tiller takes up 100 bulk space in your bag. You will also need seed packs to plant in the ground you will till. There are wheat and corn seed packs all over the world but in the greatest abundance at Bumjick Farms (near Pleasant Valley)
You will also need somewhere secure to start your garden, a walled in tamper is your best choice for this.
When you use your ground tiller 2 lumps of raised dirt will appear in the spot you used it. You then open your inventory and right click your seed, then choose plant. You can then place your seeds in the tilled lumps. You can put a max of 4 seeds per till.
Once you have your seeds planted you can use Fertilizer on the tills to help them grow faster. Fertilizer can also be found all over the map (the greatest abundance can be found at Bumjick Farms)
To apply the fertilizer to your plants you open your inventory and right click on the fertilizer then choose use.
Fertilizer spreads in a circle around where your standing and goes a good distance. If you have your tills all facing the same direction and lined up as tight as possible, the fertilizer will span out about 2-2 1/2 till out from where you stand.
Now you wait within 24-36 hours depending on weather or not u used fertilizer, your plants will be mature and ready to harvest. When you harvest you will get more seeds that what you initially planted back with your corn and/or wheat.