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Let's say I ordered seeds of a plant online. Then, I plant the seeds and grow a few plants. Then I take the seeds that the plants produced and separate them based on each plant.
Is it possible that I could then use those seeds to continue growing plants that have a desired characteristic? For example, if I wanted to grow taller and taller plants could I just keep planting seeds from the tallest plant? Or would I need to use a different method or technology to do this?
Yes, just planting seeds from the tallest plants would already do great. You could just chose an arbitrary size threshold under which you discard the seeds and above which you plant the seeds. Or you could plant all the seeds of the largest plant, almost all the seeds of the second to largest plant, all the seeds of the third largest plant etc... If plant height is a heritable characteristic (and it certainly is) then you will see a result after a few generations only.
You might want to ensure you understand the definition of heritability and the basics of quantitative genetics by reading the post Why is a heritability coefficient not an index of “how genetic” something is?.
Now instead of picking a random threshold for selection, you could be smarter and make some calculations. If you were to perform too a strong selection pressure (such as growing the seeds of the tallest individual only), then you will very quickly reduce genetic variation for height to zero and therefore remove all heritability. If you are using not a strong enough selection pressure, then you might barely see any changes even if you go on for many generations. Estimating the right type of selection pressure depends on the specific population you are facing (typically population size) and to its evolutionary history (typically previous selection on height or correlated traits and past population size).
