The first thing you need to do is take an inventory of your assets. Again it does not matter if you are in an apartment with a balcony, a half acre, ten acres, or a hundred. If you can plant things in the ground what type of soil do you have? How rocky? Sandy? How much clay? If you cannot plant something in the ground how much space do you have that you can use?
Once you have all of this in mind, you can start. Think about the things you use most. If you do not use a lot of herbs in cooking, don't bother with planting a full herb garden. If you don't use it now, most likely you will not use it if you grow it. I have seen this many times with people who plant their first garden. People will go out and plant a lot of things that they end up giving away. Again only grow things you will use.
Things that we do with the leftovers from the grocery store. Green onions can be grown perpetually from what you buy at the grocery store. Once you cut off the blades of the onions, just pop the white parts in a jar of water. Wait a couple of days to a week for the blades to start growing back. After you have seen some growth either plant them in the ground or in a shallow pot. Green onions can be planted very thickly.
The same steps above can be used for a lot of different vegetables. Table onions can be done the same way with a few differences. When you cut up the onion, cut about 1/2 inch from where the roots would have been. If you will look at the onion you will see very small "centers". Each one of these little centers can make a new onion. You can either place them in a bowl of water or actually put them right into soil. If you put it right into soil you will have to make sure it stays damp. Each onion will produce two or more new plants. This can take up to four weeks to get large enough to divide (growth rate is dependent on temperature). Table onions cannot be planted as dense as green onions, but can easily be grown in pots.
Other Items that can be grown using the same method. Celery or any of the left lettuces can be propagated in the same manner. I am sure that there are more that I do not know. If you know of more things that can be grown in this manner let me know or share them in the comments.
If you use a lot of fresh garlic, take one of the cloves and plant it in a pot. Do this every time you buy garlic for a full year. If you do this it will not take long before you have a continuous supply of fresh garlic.
Nearly all of the peppers can be grown from the seeds you cut out and throw away anyway. If you want to do this, take the core out of the pepper.You will need to remove the seeds from the core and let them dry for 24 hours. If planting in a pot,I would plant 3 or 4 seeds per pot. There is no need to plant multiple plants of the same type of pepper unless you use them a lot. Pepper plants do not need others to bare fruit. Pepper plants have what is called a perfect flower. A perfect flower means that each flower can produce a fruit.
There are many plants that can be grown in pots. So no matter what your living arrangements are you can start producing some of your own food. Warning; as you produce your own food and realize that what you grow yourself tastes better, you might just become addicted.
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Table onions sprouting from the centers as explained. There look to be at least three from this one.
Green onions at various stages of growth.