White fly may look harmless at first glance - a few little cute white insects fluttering around every time you water. But, as they reproduce quickly, they can turn into a huge white cloud of sap suckers that can destroy your vegetable patch in a few short weeks.
Don't let the name fool you - white flies are related to the troublesome aphid, and mealy bug. Don't underestimate them because of their small size either - they can gather and produce many eggs, covering entire undersides of leaves.
White flies suck sap from your plants, feeding by tapping into the phloem of plants (the living tissue that transports the soluble organic compound made during photosynthesis, like sugar sucrose, to the plant) bringing in toxic saliva and decreasing the plants overall turgor pressure (the force within the cell that pushes the plasma membrane against the cell wall) decreasing the osmotic flow of water through permeable membranes. The cells can shrink away from the cell wall and the rigid and sturdy structure of the plants is then no longer maintained. Since white flies gather in large numbers, plants that are susceptible, like leafy greens, can be quickly overwhelmed and destroyed.
White flies also secrete honey dew, which causes a sooty mold, making plants inedible.
In addition, White flies can quickly transmit and spread disease - including but not limited to cassava mosaic, bean golden mosaic, bean dwarf mosaic, bean calico mosaic, tomato yellow leaf curl and tomato mottle.
For best results in the prevention and management of white fly, it is ideal to use a combination of:
Disturbance: Spraying the underside of leaves with a medium to high pressure of water or air, and gently shaking plants for a few days in a row, can make the underside of plant leaves an undesirable place to land. This works well when numbers are low.
Soap spray: A simple spray made from a couple of crushed chillies, a few drops of grey water safe dish washing liquid, and water is very effective.
Spray on the undersides of leaves first, where white flies gather, in the early morning or late afternoon. Though I haven't noticed a problem with the solution on the plants in sunlight, I like to spray in the afternoon, then rinse off with the morning watering, in case photosynthesis is blocked.
Soap spray used on my leafy greens, causing white flies to slip off and fall onto the soil
Companion planting: Certain herbs and flowers can be inter-cropped with vegetables as companion plants to increase the protection against white flies. Strong scented plants like basil, sage and lavender repel white fly as they dislike the aroma.
Marigolds produce Limonene (the same chemical found in the peels of citrus fruits) which slows down white fly when they are flying, making them easier to spray.
There is an extensive list of flowers and herbs that serve to attract beneficial insects which are natural predators of white flies, such as hummingbirds and predatory wasps, flies and bugs; including yarrow, lace flower, dill, fennel, cosmos, Queen Anne's lace, dandelion, lemon balm and coriander. 
An example of inter-cropping of marigolds, borage, lemongrass and sage in my no-dig bed.
Exclusion mesh netting: This is the easiest way to prevent white fly as well as other insects like white cabbage butterfly. I have used this when we had a massive crop of greens with no fruiting plants, and no flowers or herbs that I could add - mesh was definitely the way to go. Ideally the mesh needs to be laid out over the area or crops before or at planting. Make sure that proper exclusion netting is used - the fine mesh that white fly can't get through and it is secured at the bottom. To ensure success it is best to triple check that there are no white flies or their eggs to begin with!
Exclusion netting on my raised beds of greens
Vacuuming: I have never tried this, though other gardeners have recommended it. All that is needed is to put the vacuum on a low setting so as not to damage your plants, carefully vacuum the white flies up and dispose of them in a way in which means that they can't fly back into the garden; for example, placing a bag over your vacuum afterwards, shaking them in, then tying it up tight and disposing of the bag into a lidded bin.
Sticky traps: Yellow sticky traps work to help stop white flies as they are attracted to the colour, however a yellow sticky trap can't tell the difference between beneficial and non-beneficial insects, so I don't use or recommend these. The idea is to move your plants to encourage flight, trapping the white flies on the strips.
Using these methods will help avoid white fly invasions in your garden.
As an added bonus, using companion planting will create more biodiversity in your garden's food web and life on a macro and micro level. Plus...it looks fantastic!