Whether direct sowing seeds or transplanting seedlings, it is important to properly space your plants within your garden in order to maintain healthy plants and encourage the greatest possible yield.
Seed packets often have a wealth of information including how much space your plants will need. For more in depth information, check out these articles.
This article from zacsgarden.com has good information and includes some handy calculators to assist you in determining the proper spacing of your plants.
This article from accessiblegardens.org also has good information and includes a video for a homemade seed spacer for square foot garden beds.