To understand how *any* topic in science is taught, you need to look at other topics, not just evolution. That is where you can understand the meanings of words like 'fact', 'law', 'theory', 'proof', etc. BEFORE the more *specific* topics like evolution, gravity, atoms, light, heliocentrism, etc.
So lets do some warm-ups before we tackle evolution.
Case 1: Heliocentrism (helios=sun). The theory that the earth and planets orbit the sun. It's hard to imagine a time when people thought the universe circled the earth, and you might think that schools teach heliocentrism now as 'fact'. But Copernicus and Galileo did not "prove" it. They looked at the behavior of the planets as an observed 'fact' and set out to *explain* that fact. And they discovered additional observed 'facts' to support that idea (the moons of Jupiter, the phases of Venus, the timing of eclipses and transits, etc.). This is why we call heliocentrism a 'theory' to this day. Not because any scientist seriously doubts that the sun is the center of the solar system ... but because the word 'theory' means *EXPLANATION*. Anything that can be explained by the idea of the sun at the center of the solar system is considered part of the 'theory of heliocentrism'.
Lesson 1: A 'fact' is not "proved" to be true ... it is *observed* to be true.
Lesson 2: A 'theory' is not a 'fact-in-doubt' ... a theory is an *EXPLANATION* for facts.
Lesson 3: Avoid the word "proof" ... use the word *evidence*.
Now, a student might be forgiven for thinking that it is taught as a 'fact' that the sun is the center of the solar system. That is so far beyond question in today's age, that nobody doubts it. But we should never forget that ultimately, it is NOT considered "proved" ... NOTHING in science is considered "proved". It is just what the overwhelming evidence points to.
In fact, it's important to remember that one of the objections used against Galileo (by church astronomers) is that it had no *mechanism*. Galileo couldn't answer the WHY. WHY would the moon stay in orbit around the earth, and the moons of Jupiter around their planet, and the planets stay in orbit around the sun. Galileo could not answer this question. That had to wait for Isaac Newton.
Which brings us to ...
Case 2: Gravity. By Isaac Newton's time, nobody was questioning the 'fact' that an apple released from a tree will fall downwards. So the image of a an apple falling on Newton's head and giving him the "idea" of gravity is iconic, but silly. Also by Newton's time heliocentrism was as close to an accepted 'fact' as anything else in science. So it is silly to think that Isaac Newton "proved" that apples fall to the ground or the the planets orbit the sun, and that this is what we call the 'theory' of gravity.
No, what Newton did was come up with an *EXPLANATION* for these facts. His insight was recognizing that an apple falling to the ground, and Jupiter orbiting the sun, are two aspects of the *SAME PHENOMENON AT DIFFERENT SCALES*. It is so easy to forget just how mind-boggling this is to understand that an apple and the planet Jupiter are two aspects of the same stuff! We take this for granted as 'fact' ... but it is NOT fact, it is 'theory.'
Again, a student would be forgiven for thinking that "gravity is taught as fact." And a careless science teacher might say that "gravity is a fact" when referring to the fact that apples always fall to the ground, and that this is called the "law of gravity" as if it is a super-duper "proved" fact.
Lesson 4: A "law" is not a "proved theory". Again, NOTHING is "proved" in science. A 'law' is an expression of 'fact' ... it is not "proved" to be true, it is *observed* to be true ... and we call it a 'law' only because we observe it to be true everywhere in the universe (we can look through telescopes and see that it applies to planets and galaxies).
Lesson 4: The same word can be used for both a 'fact' and a 'theory'. Namely, the observed 'fact' you are trying to explain (apples fall), and the theory that *EXPLAINS* that fact (a force exists between all matter). We still refer to the "theory of gravity" ... but it would be silly to think this means that the claim that apples fall to the ground is "just a theory."
Lesson 5: In nature, the same phenomenon can act at *hugely* different scales. We can look at the behavior of apples falling to the ground, and say "if gravity can cause that to happen to an apple, then a large amount of mass can cause a large amount of gravity."
Case 3: Light. This is an example of where two competing 'theories' battled it out. Our friend Newton thought that light consisted of tiny particles ("corpuscles" he called them). Others, like Huygens and Maxwell, thought that light was a *wave*. Both camps had specific experiments that showed conclusively that light had "particle-like" behavior, or "wave-like behavior". It wasn't until Einstein and Planck that we developed a new model called the *photon*, which had properties of both particles and waves.
Again it's important to remember that the photon was not "proven" ... it is not a 'fact'. The photon is a *theory*. But it would be a mistake to call it "just a theory." No reputable physicist doubts that photon theory makes an excellent *EXPLANATION* for the properties of light.
Lesson 7: Science has many cases where two competing theories coexisted ... and were later reconciled.
Lesson 8: However, it is important that supporters of the two theories have *EVIDENCE* to support them. Without *evidence*, it cannot be called a 'theory.'
So all that background is necessary to examine evolution and Intelligent Design. It is absolutely vital that students understand how words like 'fact', 'law', 'theory', and 'proof' are used accurately ... so that they are not *misused* when an emotionally charged topic like evolution comes along.
(Aside: The general topics described above are MUCH more important than evolution! And this is why it is so tragic that our science education system teaches this so badly. Every time I hear somebody utter the HORRIBLE phrase "just a theory" ... or use the word "proof" when they mean *evidence* ... or ask why evolution is "still" a theory and not a "law" ... I just cringe. I recognized yet another person who will grow up never understanding the BASICS of how science works!)
First, just like the word 'gravity', the word 'evolution' is used to describe *both* a 'fact' and the 'theory' that *EXPLAINS* that fact. The 'fact' of evolution is the idea that species *change over time*. Period. That is not "proved" to be true ... that is *observed* to be true. No reputable scientist seriously doubts it.
But no reputable scientist seriously doubts that Charles Darwin's theory of natural selection provides an excellent *EXPLANATION* for the fact that species change over time. So people who call it "just a theory" are just confused about basic science. The 'theory of evolution' is not the 'claim-in-doubt' that things evolve (change over time). The theory of evolution is the explanation for WHY things change over time. And it is also all the other things that this same 'change over time' explains. Like the origins of species (which is where Darwin got the title for his book).
Darwin's insight into evolution is similar to Newton's insight into gravity ... namely that the SAME PHENOMENON CAN OPERATE AT HUGE SCALES. Just as Newton proposed that large amounts of mass can produce large amounts of gravity ... Darwin proposed that large amounts of TIME can produce large amounts of CHANGE (evolution). And that this explains why there are so many, significantly different species.
So is evolution taught as 'fact'? Well the idea that species change over time is taught as fact because it IS fact ... observed fact.
But the question you are asking is whether the idea of shared ancestry as a consequence of that change-over-time is taught as fact (as this is what Intelligent Design challenges ... not the FACT that species change, but the explanation for WHY species change).
And in that case you could be forgiven for thinking that this is indeed taught as 'fact' ... and a careless teacher or book might leave that impression.
But it is more correct to understand that the theory of evolution is called a 'theory' because it is the best *EXPLANATION* for the fact of evolution (the fact that species change over time).
So what about Intelligent Design? There is absolutely nothing wrong in science with considering competing 'theories' ... but to be called a 'theory' it needs to have *EVIDENCE*.
It is not enough to claim to have evidence *against* Darwinian evolution. You need to have evidence *in favor* of an Intelligent Designer. Some way of testing whether such a Designer actually exists.
(Aside: I am NOT an atheist ... my point is to ask whether there is *EVIDENCE* of ANY 'Designer', God or not, that has the capacity and motive for doing the kind of small-scale tinkering proposed by Intelligent Design advocates.)
I sincerely hope that helps.