I have found that the only way to really learn plants is by
experience. Have someone show you the plants they know, and bring along a field guide (I like Peterson's guides) for reference. Take your time - I find that I can only learn so much in a season, and every year I add a few plants to my repertoire. Use your own
yard and the farm you help on as classrooms - at the beginning of the season, pay attention to what plants look like coming out of the ground, and what they turn into. This spring and summer, having moved to a new homestead, I let a bunch of "weeds" come up in my garden, letting a few get big and go to flower. Now I know the difference between my
volunteer poppies and thistles (which look surprisingly alike as seedlings), and I know which one I'm more interested in encouraging.
There are certainly
books and websites that can help you learn (the aforementioned Peterson's and this site are two good examples), but the problem with looking at pictures of plants is that the actual plant tends to look different, depending on growing conditions, the area you live in, etc. Plus, some plants are biennials, and look very different from the first year (basal leaves and big taproot) to the second (tall, flowering). So, again, get the experience of watching particular plants through their whole life cycle. Then, try to find these plants in other places. I promise that you'll start seeing differences through experience.
Some of my favorite and easiest plants to start with: plantain, dandelion, red and white clover (two similar plants with particular differences in color and growth pattern), wild carrot/queen anne's lace (but be aware of its poisonous look alikes!), burdock, comfrey. Take the time to learn the differences between the conifers - lots of regular non-permie folks call them all Pine, and think that Hemlock is poisonous, and learning the difference totally changes a walk in the woods!
That being said, here are a few tree keys online:
http://www.arborday.org/trees/whattree/
http://www.oplin.org/tree/index.html
And a great book about learning botany, which is important to help you use field guides more effectively(and also learn more about plants in general):
http://www.amazon.com/Botany-Day-Patterns-Method-Identification/dp/1892784351