Before I even start with evolution the basics of science must be covered. There is no one single "scientific method" written in stone. But the following flow chart is a very good basic model to follow. Again, variation from this is allowed, but one must be willing to support one's claims at the very least to be following this method:
As you see it all starts out with questions. Some of them are easier than others. "Why does it rain?" is a rather easy one, even though it is more complex than the simple answers given in grade school. "What is the meaning of life?" is an example of a question that may be outside of the ability of the scientific method to answer. One cannot answer all questions with the scientific method. It is pretty much limited to the physical realm. And even some of those questions may not have an ultimate answer. For this thread the basic question will be some variation of "How did the life that we see today get to its current state?" Much of that can be answered.
Background research is educating oneself about as much as possible about what is already known about the topic one is asking a question about. That can include all of the education one has had over one's life. Doing background research also often involves gathering existing data. Please note, that as one does this research the original question may be altered.
Next is perhaps the most important step in the scientific method. One needs to construct a hypothesis. This simple flow chart does not openly state, this but the implication is rather obvious, the hypothesis needs to be testable. To be a scientific hypothesis that is the number one condition. It must be falsifiable. That means one needs to have a reasonable test that could possibly refute it if it was wrong. We will be getting back to that.
Next one has to actually test one's hypothesis. One needs to try to refute it. Sometimes one's test simply does not work The hypothesis may just need to be tweaked a bit. That happens quite often in the sciences. So one goes back, reforms one's hypothesis and tests it again. Eventually one will hopefully get clear data and we can move on.
Now we are approaching the finish line. What does your data say? Does it confirm the hypothesis confirmed? Did it manage to avoid being refuted? Good. Then one communicates what happens. Did it fail? Then one will need to go back to the formation of a new hypothesis using the knowledge gained in the failure of the hypothesis. This is an important step that is far too often ignored. Failed hypotheses are often key to understanding an idea. It is the failures that lead to our successes. If a scientist never fails he is probably not contributing much in the way of science. Safe questions do not lead to new knowledge. Real scientists are not afraid of failure.
Either way the "last step" (scare quotes used because this is often only the beginning) is to communicate one's results. Today that means going through the process of peer review in a well respected scientific journal. One's peers first check the article for obvious flaws and that it is original work that has not been already done. If it passes it is published and now the real testing begins. Scientists are a skeptical lot and they will often tear apart the work of others. If the original scientist made a mistake that he or she missed and that the review panel missed it is apt to be discovered by other scientists that work in the same fields. Merely publishing and article does not mean that one is right. It only means that one is not obviously wrong.