You can use organic or inorganic materials to mulch your garden. Here is a list of some options and usage tips.
Lawn Clippings: Don't use clippings from a lawn that has been treated with a herbicide or weed killer because those chemicals can kill your vegetable plants. Let untreated clippings dry before putting them around your garden; fresh grass gets to compact and smells bad while it's decomposing.
Sawdust: Sawdust is often available for the asking, but it requires added nitrogen to prevent microorganisms from depleting the soil's nitrogen supply. If possible, allow sawdust to decompose for a year before using it as a mulch.
Straw: Straw can be messy and hard to apply in small areas, but it is an excellent mulch. Just don't use hay, which many weed seeds.
Organic mulches:
Compost: You can use fully or partially decomposed compost (it is better if the compost is fully decomposed). Compost makes a great mulch and soil conditioner.
Lawn Clippings: Don't use clippings from a lawn that has been treated with a herbicide or weed killer because those chemicals can kill your vegetable plants. Let untreated clippings dry before putting them around your garden; fresh grass gets to compact and smells bad while it's decomposing. Leaf Mold: Leaves are cheap and prolific, but they can blow around and be hard to keep in place. Ground up, partially decomposed leaves will stay in place better. Nitrogen should be added to leaf mold. Note: Don't use walnut leaves. They contain iodine, which is toxic to some vegetable plants.
Sawdust: Sawdust is often available for the asking, but it requires added nitrogen to prevent microorganisms from depleting the soil's nitrogen supply. If possible, allow sawdust to decompose for a year before using it as a mulch. 
Straw: Straw can be messy and hard to apply in small areas, but it is an excellent mulch. Just don't use hay, which many weed seeds. Wood Chips or Shavings: Wood chips, like sawdust, decompose slowly and should be allowed to partially decompose for a year before being used as mulch. Additional nitrogen will be needed to supply bacteria during decomposition.
Inorganic mulch:
Landscape fabric: used in small gardens for plants that are grown in a group or a hill, typically vining plants such as cucumbers, squash, or pumpkins.
It can also be used for individual plants such as peppers, tomatoes, and eggplants. Because the fabric is black and attracts heat, it should not be used for crops that need a cool growing season -- cabbage or cauliflower, for instance -- unless it's covered with a thick layer of light-reflecting material, such as sawdust.
