Today I'll explain the basics of farming.

Pt. 1: Farming Underground
Like anyone should know, when you are beginning to farm you'll need supplies. For a underground farm, you will need at least 5 seeds (of any kind, but regular seeds are easier), a pick, a shovel (Optional, but recommended) dirt, a hoe, and 1 or more water buckets.
Once you have your supplies, you need to clear out space. Just mine/dig out the area needed to farm. (4 by 4 is a good amount, or 6 by 6) Once you have your space, mine out the bottom. Now, place dirt where you mined. The next part is tricky- because you want to make the most of your space, (and water can moisturize up to 4 blocks) dig a trench every 4 blocks. Because you don't always get enough room to make that method look nice, you can try another method. All you do is dig a trench every other block. By the way, the trench should go horizontally. and should be only 1 BLOCK DEEP. Now, you need to add the water. Fill the trenches up until they're all nice and level. (You will need to go and collect more water, probably) Next you need to hoe the dirt. Once all the land is hoed, plant the seeds. (You may need more.) And there you go! Your farm is done.

Pt. 2: Farming Outside
Most people farm outside. It's really not that different except you don't need a pick and you need fence because animals can trample the crops.
Like underground farming, you might need to clear out space because farmland needs to be flat. After you have your land, dig out your trenches and fill them with water. The next thing you need to do is hoe the land. After that just plant your seeds. But, there is another step! You need fencing. So you need to craft some fence. The reason I don't like this is because it can be costly- you need 6 sticks per two fences. To make fencing, all you need to do is place three sticks in the 1st row (the bottom row), and three sticks in the middle row. After you have enough fencing place it around the farm. Then you need to get in, so make the same crafting recipe BUT you need to replace the two sticks in the middle with wood planks. Now you have a gate. Place the gate where you please. (You might need to remove a fence.)

Pt. 3: Managing and improving your farm
Now that you have your farm, you will need to replace seeds over time. However you should get enough from when you harvest your crops.
There are actually many ways that you can make your farm better. You can plant a different type of seed, but to obtain these seeds you need to find a patch of pumpkin, or find melon seeds in a mineshaft. If you find any, you can make seeds by placing the drop they give into a crafting tile. The problem with these type of seeds is that they need one block for the stem and another for the actual harvested item. So, you need double the space.
Another way to make your farm better is to just add more area to it. You can make more fence, remove some of the old fence and make the area in the fence bigger and then dig out more space if your farm is outside, or you can just dig out more area if you're underground. But the only problem is you need more water because the water needs to be level with the dirt block for the seeds to grow and the plants need water.