Seeds can be very fascinating because of all the shapes, sizes, and colors. These attributes can make it difficult to differentiate seeds from the dead, dry flower parts that remain after pollination and development of that seed.

In the beginning, do not concern yourself with what the seed is on plants in general. The best thing to do is learn about the seed production of the specific plants that you want to know about. Many books and websites are available that will discuss everything about a certain plant, including how it produces seed and what the seed looks like. Many include actual images of the seed, often magnified. A little research goes a long way. Check out this example of a very good online resource and note the image of the seeds: USDA.gov

If the plant variety is known one can do an online image search and often get good results. For example, if one does a Google image search for "impatiens seeds" some nice images and links will result. A person can then use the information gleaned to properly identify and harvest the seed from the plant in question.

Now, no offense, but I do not know what education level you are at. If you do not understand the plant cycle of seed to bloom to seed production then you will need to research how a flower produces seed, and go from there. Start with Flower Wiki and proceed to Seed Wiki and they should get you started.

Have Fun!
-Tom

All of the above but also just spend time with your plants observing them. You will begin to get to know when they leaf out, flower, set seed and you will gradually build up an understaning of their characters. Plants are all different and, as soilent said, get to know the ones you are most interested in. Half the enjoyment of gardening is this understanding of your plants and being in tune with their seasonal cycles.

There is a wonderful book called Botany for Gardeners that most libraries have. It has great drawings and explains how plants grow for real. Prepare to be addicted to seeds..