So, what exactly is science? Is art science? Is math a type of science? Science is one way to learn about the world. Science is orderly, based on facts and calculations, and is a good way to evaluate matter and energy. Science cannot do everything though. Science cannot make value judgements, and is not a great tool for imagination, opinion, or ideas outside of the physical world.
While science cannot do everything, it is a very useful tool. Like any tool, there is a time to use it. For example, it is a mistake to use a hammer when a screwdriver would work better. When should you use science? To better understand what science is, let's compare it to non-science and pseudo-science.
Science
For something to be considered a science, it must be proveable, measurable, and repeatable. Anything that fits into these categories would be considered science. Let's take baking for example. Is making a cake proveable, measurable and repeatable? Yes. That's the science of baking. There is also an art to baking which involves tinkering and experimenting and opinion. The more precise the proofs and measurements are, the "harder," or more firm is the science. Mathematics is considered the most exact of the sciences, followed by physics. Chemistry comes shortly thereafter, with geology after that. The "softest" of the sciences are biology and ecology. It's harder to repeat and prove some of the ecological claims, but as the evidence grows, the claims become more stable.
Non-Science
A subject is non-science when it does not attempt to be proven. Many things in life are not proveable or measurable, and that's ok by me. Emotions fall under this category, as does art, religion, music, opinion and anything that can't be proven. How do you prove hope? Is liberty measurable or repeatable? How much does joy weigh? See, none of those are scientific, and that's all right. You can't put Shakespeare in a formula, and you can't calculate the beauty of a sunset.
Pseudo-Science
Sometimes there are fields of study which appears to be scientific, but lack one or more of the qualifiers. For example, let's talk about the existence of aliens. While there are people who claim to have seen aliens, it is not proven, as far as the academic world is concerned. There is no specimen which scientists can look at, make measurements, poke and prod about and verify its existence. The study of aliens is then considered a pseudo-science. It looks like science, but it's not.
Pseudo-science can also be when people take something non-science and try to prove it scientifically.
It can also apply to parts of science that aren't yet proven. Can something move from pseudo-sceince to science? Sure.
If we found the real Loch Ness Monster and it could be verified to exist, it would no longer be considered pseudo-science, but science.
Until then, Nessie remains in that in-between world.