Which plants can be grown at home in monsoon?

It is nice that you wish to plant and grow some vegetables at your home in this Monsoon.
It depends how much spare land you have. As plants need some amount of sunlight and water, you have to grow them at open places where you get both. As pots have short spaces for the roots to grow deep and spread, you have to select such plants which take less time say about the three or four months of Monsoon.
The plants should grow to short length, the vines should not spread too far etc, Hence where space restrictions are there you can grow Ladies Finger(Bhindi), Brinjal, Bitter gourd(Karela), Snake Gourd(Padval), Green Chillies ,Legumes and beans like Sem Phali, Spinach varieties, Tomatoes etc.. In case you have sufficient space as backyard, then you can grow pumpkin, cucumber, bottle gourd etc. Tubers like Beetroot, Radish, and Carrots also can be grown with proper preparation.
You can use cow dung manure if that is available esily at your place. Otherwise compost manure can be used. You may also use some general multipurpose herbal or natural insecticide and pesticide. You may ensure adequate water but not high water retention also. If you have a habit of composting your kitchen waste then that is good manure.
Depending on the place and quantum of rains etc you may need some adjustments. You can get the general guidelines from a nearby fertiliser shop or even your vegetable vendor coming from the village.

You want to have plants in pots or in the open land. Anyhow, monsoon is a good time to start this plantation. Many people will start this activity in monsoon.
For any plant to grow well and fast, the requirements are air, water and sunlight (moderate). So if you want to plant these plant in pots also choose a place to place them in your house where there will be good air and sunlight. Watering can be taken care of by you when the need arises. If you have open land and putting the plants in that area, you can have a drip irrigation system so that watering will be easy and consumption will also be less. Amazon will be supplying all the required components for this drip arrangement and you can order them online.
Any type of vegetable plants you can grow in the house and leafy vegetable plants also you can grow. The selection of these plants will depend on the place available for you. If you have sufficient place you can go for Donda, bitter guard(Kakara), pumpkins, bottle guards etc. Otherwise, you can go for Ladies' finger, brinjal, green chillies, tomatoes, and other regular use vegetables can be grown.
If you have sufficient land you can make the compost and use that. Dung can be used as a fertiliser. You should take care of the plant properly and use insecticides and pesticides as required. They will be available off the shelf in any fertiliser shops.

If you have a garden outside your house or a piece of land adjacent to your house or space on the rooftop for some flower pots or even some space in balcony to keep some flower pots, then you can pursue your hobby of gardening. First thing in gardening is to remove the stones and boulders from the soil and make it smooth. Generally people either go for vegetable planting or flower planting or a mix of both depending upon the location of the land or flower pots.

During monsoon there is enough humidity in the surrounding and water is available for plants and in such a season there are various big sized as well as small sized vegetables which can be easily grown. Some of the common vegetables which are grown during this time of year are Lauki (Bottle Gourd), Tomato, Karela (Bitter Gourd), Carrot, Tinda (Indian Squash), Parwal (Pointed Gourd), Sem Phali, Tubers, Cauliflower, Kantola (Teasel Gourd), Radish, Cucumber, Beans, Bhindi (Okra) etc.

If your interest is in flowers then some of the flowers which can be planted during monsoon are Balsam, Marigold, Cosmos, Sunflower, Zinnia, Cleome, Salvia, Portulaca, Ageratum, Cocks comb etc. These flowers have beautiful colours and can give the place an ambience of superior kind.

Whether it is flowers or vegetables, it require some fertilisers for the good growth of plants. There are many types of fertilisers available in market specifically for these plants and can be used accordingly. NPK (Nitrogen, Phosphorous and Potassium) fertilisers are very common and are used by many garden hobbyists. NPK fertilisers come in various ratios but 5-5-5 NPK would suffice for your purpose and about 1 Kg of this is sufficient for 100 sq. ft. of garden. If you are using organic manure then the rule of thumb is to use about 10 kg of it for a 100 sq. ft. of garden. It has to be evenly applied to the soil. If you are composting yourself then you can also use that in place of the organic manure.

All good suggestions are already posted in the above responses. I would like to add a bit from my own experience.
1. You can easily grow a Tulsi plant in a small pot. It grows really well in monsoon and has many benefits for us. Secondly, you cannot but Tulsi leaves from market on a regular basis. So better grow it and use the leaves as and when required.

2. Coriander, mint, spinach, etc can be grown very easily during monsoon. They require very little space to grow. I have spinach and mint plants in my balcony and they grew very fast.

3. Spring onion and garlic can also be grown very easily. I have grown spring onion in a plastic bottle half-filled with water. Here the onion tuber must not be soaked in water.

4. Lemongrass is my favorite ingredient for tea. I have grown this also in my balcony and it has grown well.
In all the cases, exposure to sunlight is required and watering should be done through spraying and in small amounts.

If we have enough space in the backyard, we can exploit the opportunity to grow some of vegetables and eye catching flowers at our homes in this monsoon-
1) Ladies Finger ( Bhindi) - It is one of the most favourite vegetables for both the children and adults alike. This requires a warm and humid weather to grow.
2) Baingan ( Brinjals) - This vegetable has different uses in our kitchen such as making vegetables, preparation of sambar or Bharata etc
3) Carrot ( Gajar) - One has to choose a good variety from a farm in order to grow them in our garden so as to have a supply of juicy carrot.
4) Radish ( Mooli) - This vegetable is easy to grow having its different shapes and sizes. This would cater to our needs both in the form of raw salads or in the form of vegetable.
5)Palak ( Spinach) - It is highly nutritive in nature having plethora of benifits.
6) Cucumber ( Kheera ) - It is the best choice to grow in the monsoon. It requires porous soil and plenty of sun so as to have healthy supply of veggie throughout the year.
7) Tomato - This vegetable is versatile in the sense it can be used in the different type of vegetables. It can grow even in the scanty supply of water.
Some area of the land can be reserved for the plantation of flowers so as to create an amazing look for the viewers. Some of such collections are as follows -
1) Hibiscus - Hibiscus is very easy to grow and this will provide a decent look.
2) Lily - It requires a pond in the garden to grow lily. This flower looks exotic and can be grown in this season.
3) Jasmine - Jasmine if added in the garden would provide sweet smell around the area because of its intense fragrance and due to its scent it is known as Rajnigandha.
4) Balsam - It comes in different variant such as violet, white, pink and blue.
5) Cosmos - Cosmos flowers are very beautiful and are used for the decoration purpose.
6) Sunflower - It looks amazingly beautiful and this giant looking flower look very attractive and vibrant.
We need some sort of supplements to strengthen the soil with the addition of NPK fertiliser which comes from different variants indicating the percentage composition of nitrogen, phosphorus and potassium.
Nitrogen content will provide leafy growth and the stem portion will be nurtured. Phosphorus is essential for seed germination and root development such as Carrots, Turnips etc.Presence of potassium will help the steady development of the plant and would resist disease. NPK may show its its chemical composition such as 5/5/5 indicating nitrogen, phosphorus and potassium respectively. Get the soil tested prior to application of NPK variants to choose the right blend.
Natural manure may also be applied to strengthen the soil health such as cow dung, vermicompost etc.