what is the scientific method?

So you have two questions here, I'll start with the first.

The scientific method is a way to verify our observations and assumptions in the world through experimentation. Specifically it is a framework for designing experiments so that we can arrive at a high level of truth and accuracy.

You always begin with a hypothesis, which is just an unverified explanation for why you think something is occurring. So for your experiment you are testing photosynthesis, which is the idea that plants derive their energy from the sun. So how can we design an experiment to test this.

At its most simple you can take two plants and allow one to grow as it normally would outdoors. This is your control. You can take another plant and place it in the closet. You can then take measurements of each plants growth each day and record your findings. If plants derive their energy from the sun, the plant in the closet would fail to grow.

Now there are a few caveats. What if the plant outside dies? What if you are watering them different amounts? What about soil quality and fertilizer? All of these things could alter your findings. You need to make sure that all other conditions are equal with the exception of sunlight in order to make sure your results are as accurate as they can me. You also don't want to use just two plants because any number of conditions could give you false positives or negatives. Real scientific experiments are repeatable and usually you want as big a sample size as you can get. So if you can do this with thousands of plants of different species your results can be even more accurate.

For a school project though usually just a few plants will suffice. You can take it one better and do some plants under artificial light indoors as well and see how they fair.