Weed identification begins with garden plant identification. There are thousands of plants that we typically consider weeds, but you don't need to learn even a fraction of them. There are far fewer plants that we cultivate in our gardens; it is much easier to learn what they look like. Learn what a cucumber, corn, squash, pea, radish, lettuce, and carrot seedling looks like and you're well on your way to learning weed identification.
The basic premise is that you become familiar with the plants you're intentionally growing. If anything else pops up next to your chosen few, it's a weed.
How do you know what a cucumber seedling looks like? The answer is to sow cucumber seeds in a discernible pattern. As they grow you'll see the small plants lined up as you planted them. Those are the cucumbers.
Want to learn about green beans? Grow green beans. You'll see a collection of plants growing at the same rate because you planted them at the same time.
As you care for your seedlings, transplants, and established plants, remove any invaders before they become established. It may be Milkweed, Spurge, Purslane (my nemesis), Sorrel, or Thistle that moves in. While experienced gardeners can often identify such culprits it really doesn't matter as they are plucked from the soil. Pull them early and pull them often. Keep your garden bed for your intended plants only.
Eventually, as you maintain this basic regimen, you'll become familiar with which plants are the most common weeds in your garden. You pluck them from your beans and peas and then you'll see them among your daisies and poppies. You won't have to struggle deciding if it's a weed or not, you can be confident in eliminating the threat.
Of course keeping up with the attack of weeds can be daunting. Use that to your advantage. When one of your beds is overrun, remember what the attackers look like when you eventually deal with them. This can help in their identification in other beds.
The internet, reference books, local Extension offices, and experienced gardeners can all help you identify a plant. In my case I learned that my weed nemesis was "Purslane". The waxy leaves, low growth pattern, and green-purple color became very easy to spot in the garden. I learned that purslane is edible and is often cultivated by gardeners as a salad plant. I also learned that it is resistant to many of the herbicides I would have used on it. The best method of eradication was pulling or cutting it before it seeded.
Pay attention to everything in your garden. We typically don't sow seeds in our garden paths. If something begins popping up between our stepping stones or through the mulch, it is a wild plant that was sown by wind or birds or was lying dormant in the soil for untold years. Take a few seconds to make a mental image in your mind and store it in your brain's "weed file". The next time you see that plant in a garden bed you won't need to hesitate. It's a weed.
Even plants you place intentionally can become weeds. Remember, a weed is any plant growing where you don't want it. You want them in your garden, but they can self-sow or spread to an area that isn't part of your plan. Once they interfere with other plants and you don't like their location, they're weeds.
You're probably more familiar with this category of plant so identification can be easy. My Lamb's Ear (Stachys byzantina) is nice to look at and fun to feel, but one section has overrun my Knautia and Salvia. It's turned into a weed and needs to go. Lucky for me I can easily tell the offending plant from the others I'm trying to save because it's one I planted on purpose. The Knautia in this bed is also beginning the march into other areas. Right now it's a valued plant but I recognize that it will become a weed once it escapes into nearby plantings.
Identifying weeds can be quite easy, but identification doesn't imply knowledge about the nomenclature, history, cultivation, and life cycle of a plant. You don't need to know the name to identify a plant as a weed.
Don't delay dealing with a problem plant while you learn about it. Know the plants you want in your garden. Learn about their cultivation and maintenance needs; know their nutrition and fertilization requirements; know their names. Realize that any plant interfering with your garden is a weed. You can learn its name after you remove it.