There are dozens of kinds of vine weeds. Some are specific to a particular state and others are spread throughout the country. Vine weeds are particularly aggressive, making them difficult to control with herbicides. In addition, some vine weeds have toxic properties. Thus, it is important to identify the specific vine weed growing in your yard so that you can design an effective plan of attack.
Use the flow chart found at the University of Missouri Extension website. A link is in the Resources section. You will be asked to identify several key characteristics. For example, does the weed have three leaflets or is it divided into three lobes? The flow chart will direct you to the appropriate vine weed.
Pick up a weed identification book from your local library and take it out to your yard with you. There are a number of weed identification books, including "Growers Weed Identification Handbook" by Bill Fischer, "Weeds: A Golden Guide" by Alexander Martin, and "Invasive Plants" by Sylvan Ramsey Kaufman. Keep in mind that these books are general guides. You may have greater success if you pick up a regional guide that is specific to the weeds that grow in your geographic area.
Visit the USDA National Invasive Species Information Center. There is a link in the Resources section. The USDA National Invasive Species Information Center contains lots of useful information. For example, you can view pictures, by state, of common vine weeds, and find private and federal grants to help pay the cost of having an expert come out to your home, identify the weeds and help you design a plan to control them.