Companion planting is when you plant different types of plants beside each other so they will help ward  off diseases and hopefully pests and even attract beneficial insects so you will end up with a healthy,thriving ,lovely green garden.

This method of gardening is particularly attractive to the organic grower where they may be able to keep pests and diseases at bay without harmful chemicals.
I wont waffle on any more other than give you the inportant info on what to plant and where to plant it.
Some gardeners will look at this list and say "oh no, thats not right",but I will say again EVERY garden is different in every part of the country and the world. The same way bees gather pollen locally to make honey locally and that then can be used as a remedy to help keep hay fever at bay by the local people,Im sure the same principal works for companion planting. 
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Asparagus -----Parsley, capsicum, basil, lettuce and tomato 

Basil----- Tomato, most vegetables and herbs 

Beans----- Potato, corn, lettuce,  cucumber, strawberry, celery, carrots, cauliflower, radish, spinach, 

Beetroot----- Onion, lettuce, spinach and silver beet 

Broccoli----- Onions, leeks and celery 

Brussells Sprout -----Potato 

Cabbage----- Onion 

Carrot----- Peas, leeks, lettuce and chives 

Cauliflower----- Onions and leeks 

Celery -----Tomato, leeks and beans. 

Corn----- Lettuce, peppers, cucumber, beans and peas 

Cucumber----- Radish, lettuce, beans, peas and artichokes 

Leeks----- Cabbage, celery, onion and celeriac 

Lettuce----- Beetroot, strawberry, radish and corn 

Mint----- Cabbage and tomato 

Onion----- Lettuce, cabbage and carrots 

Parsley----- Tomato, asparagus, carrot and peppermint 

Parsnip----- Shallots, chives and lettuce 

Peas----- Cucumber, radish, turnips, corn, carrots and beans

Pepper Chili----- Cucumber, squash and lettuce 

Potato----- Tomato, cucumber, sunflower, green beans, peas and broad beans 

Pumpkin----- Corn 

Radish----- Peas, lettuce and nasturtium 
Shallots----- Carrots, beetroot and mint 

Spinach----- Strawberry and most plant 

Strawberry-----  lettuce and bush beans 

Tomato----- Asparagus, peppers and basil 

Zucchini Courgette----- Parsley, tomato, silver beet, spinach, squash, corn and capsicum