What is a weed? Well, it depends on your point-of-view. From a human's perspective, a weed is any plant that's out of place in your garden, and therefore should be removed. From nature's perspective, weeds are highly succesful plants that dominate wide-open spaces due to their adaptability to adverse conditions, and effective means of reproduction (they tend to produce tons of seeds - think of those dandelions you blew on while making a wish!).
Having said that, weeds will compete with your valuable plants for nutrients in the soil, and spread throughout your garden plot if left untended. The trick is to be able to identify weeds from your chosen plants - especially when they are all at seedling stage and can seem close to identical. When planting your seeds, be sure to use plant ID's; it is also helpful to plant in rows. If you are out in the garden and have any doubt, ask - before clearing an entire area, you might want to pull a sample and bring it to an experienced gardener, or compare with these pictures, and possibly others in a field guide.
Overall, you will find that when it comes to weeds you really do learn from experience. Below is a catalog of common weeds that you will likely encounter in your garden.
The one upside to finding weeds in your garden? Some are edible - and highly nutritious! Foraging for wild weeds can be risky due to contaminated pesticides or soil, but when weeds pop up in your own garden bed, you know that they have been grown in a healthy environment.
Purslane comes from India, where it was a food crop centuries ago. According to legend it was Gandhi's favorite food. Now it grows in all 50 states and Canada.
Eating purslane: It's loaded with vitamin C, beta-carotene, vitamin E, and antioxidants, not to mention its richness in the omega-3 fatty acids that have been linked with lower cholesterol levels. Purslane tastes a bit like spinach; like spinach, this weed is edible raw or cooked. Add tender shoots to soups or garden salads.
Pigweed, or amaranth, is actually an herb that has a discriminating taste for rich soil. Thankfully, it has a shallow root system and is very easy to pull up by the root. If you toss it anywhere near your compost pile you can expect to have a crop of it fairly quickly, so it's best to dispose of it with yard waste. Tilling the soil with a garden hoe or rake so that the seeds are buried deep usually eliminates this weed for an extended period of time.
Lambsquarters is one of the most tenacious weeds around. Like pigweed, it has a preference for rich soil, compost piles and fertile garden beds. It’s an annual that reproduces by seed during the early spring season, but once established you will find it in your garden throughout the growing season. Lambsquarters is easy to identify once you get the hang of it. Thankfully, it pulls up very easily by the root. Left to its own devices these weeds can grow quite tall to blend in with flowers. It’s best to pull them when you first see them break through the earth.
Eating lambsquarters: Lambsquarters are a good source of amino acids. The leaves and stems are edible, with a taste that can be compared to spinach or chard. the easiest preparation is to simply steam the leaves and stems in a small amount of water until tender. The greens will cook very quickly and turn a dark green color as they shrink down during cooking. The young leaves and smaller stems can also be eaten raw in salads.
Dandelion. The bright yellow flower of a dandelion makes it easy to spot. The best way to eradicate this common weed is to pull it up by its roots.
Eating dandelions: Dandelions may be common weeds by day, but prepared like other greens, they are considered gourmet fare by night - and nutritious! According to the U.S. Department of Agriculture, a serving of uncooked dandelion leaves contains 280 percent of an adult's daily requirement of beta carotene as well as more than half the requirement of vitamin C. Dandelion greens can be tossed into a salad of mixed greens, or sauteed and served like any other bitter green, such as escarole.
Quackgrass, or witchgrass, is very easy to identify. It grows very tall (1-4 feet high),and once it gets a head start it is nearly impossible to eradicate. Quackgrass grows from underground rhizomes deep in the soil, and so you will have little luck just pulling it up. This weed has been known to find its way through pavement.
Daisy. You may be surprised to learn that daisies are classified as weeds. Perennial flowers with similar heads are of course in high demand, but this innocent looking flower is considered to be an invasive weed. Fortunately, the daisy's roots are very shallow and tend to clump so that it can be easily dug up. Left untended, weeds cast themselves to form large patches. As weeds go, they are not the ugliest nuisance in the garden and they are by far one of the easiest to eradicate.
Evening Primrose has a sturdy stalk, and left uninterrupted can continue to develop to heights of 4-6 feet high. Relatively quickly a bloom appears, then another and another; unfortunately, the flowers are not up to the standards of its spectacular stalk. The first time you have one of these charmers in your garden it may take some convincing that you do in fact have a weed, however, once you allow one of these weeds to come to fruition you will quickly note that it really is not worth cultivating. They pull up easily and will not multiply if you eradicate before it blooms.
Eating evening primrose: All parts of the plant are edible. The leaves can be picked and used cooked or fresh, but they are quite pungent and slightly hairy. 
Chickweed forms a mat or ground cover and tends to spread most vigorously in the spring when it has the least competition. This seemingly benign weed may seem like a blessing in bare areas of your garden, however, it has a tendency to mingle closely with wanted ground cover plants, stealing valuable nutrients. Once chickweed gets established it is hard to pull it out from the roots of your other plants. A favorite food of chickens (hence the name), humans have little need for it so pull it up if you can. Your next best alternative is to till the seeds deeply into the ground. Seeds will only germinate in shallow soil.
Eating chickweed: Chickweed is known to have many medicinal properties and is often recommended as a weight-loss aid and for skin irritations.Vitamin rich chickweed can be steamed or cooked as an ingredient in soups, but probably the most popular culinary use is simply as an addition to green salads. Harvest the plants when they are lush, green, and full, including the tender stems, buds, and flowers, right along with the leaves - they’re all edible! It can also be dried and used in herbal teas.
White clover, also known as shamrock, brings us luck of course, but only if you happen to find a four-leaf clover (the odds are 1 in 10,000). Clover is no doubt one of the most common weeds in gardens and lawns. Pull it up by hand in your garden plots. In lawns, some choose to let it grow, as it chokes out other more annoying weeds, stays green while grass turns brown, and requires far less water than an all-grass lawn. The downside is that clover is not pretty when growing in an otherwise unform carpet of grass. It also quickly gets out of hand growing between walkways and fences.
Eating clover: Clover is a good source of calcium, chromium, magnesium, niacin, phosphorus, potassium, thiamine and vitamin C. When you and tender, the shoots and greens can be tasty either raw in salads or as cooked greens. 
Ragweed can be spotted from some distance away by the symptoms it produces; it is estimated that 2 out of 10 people have an allergic reaction to ragweed, causing sneezing, itchy eyes, stuffy nose and sore throat. Symptoms appear late summer and fall when one billion ragweed pollen grains become airborne. If you can pull the weed up before it turns to seed then obviously this is the best tactic to take. However, if this is your chosen remedy then be sure to wear protective gloves. Contact with skin has been known to cause allergic reactions in people who may have an unknown sensitivity to ragweed. 
Hawkweed looks very similar to the common dandelion except that it is quite a bit taller (1-3 feet). Colors may range from yellow to orange or even red. It is so-named because popular myth was that the hawks depended on the weed to improve their keen eyesight. Not to be confused with the native flower of the same name, this noxious weed has been on the hit list of environmentalists for quite some time. It reproduces via runners that stem from underground rhizomes, and its fast reproduction threatens to dominate indigenous plants, now threatening to irrevocably upset delicate ecological balances. Scientists have found that it is even adapting its growing conditions by growing in shady wooded areas in addition to sunny locations. Pull them immediately if you spot them as no natural herbicides/methods of eradication have been developed.
Curly Dock will not go without a fight. It has a large taproot that will actually re-sprout even when broken. If you tug on this weed you will feel its resistance immediately. It may be identified somewhat easily because it often grows in clumps and its leaves are usually tinged in red. The best way to get rid of this weed is to use a shovel or hoe and dig it completely out of the ground. Organic herbicides have been known to work in the fight against this weed. Specifically, those with clove oil have been proven remedies.
