{ Please note that I'm NOT the author.
Yesterday an anonymous person (with username Ornlu_Wolfjarl) on Internet described our "common cold and fever" in such an amazing, yet factual way that it boggle my mind. It was highly appreciated by doctors, and biologists alike.
However, unfortunately user deleted the response. Donno why.
I recovered it from Google's snapshot. And, decided to "save" it myself. }

How does a virus work?

Imagine that the virus is an envelope made of protein and it contains a small piece of genetic material (can be DNA or RNA). It's not an actual living cell. It doesn't breathe, eat, sense or even reproduce. The only way it can reproduce is if it hijacks a real living cell's reproduction mechanisms.

And that's how all viruses work. They enter your cell, their envelope breaks, and their genetic material is inserted into the cell's genetic material. The cell then "thinks" that the new genetic material is some important protein that needs to be constantly produced. So that's what it does. It keeps producing it. The proteins being produced are actually the ones required to create a new virus particle. They are the envelope + some helper proteins that copy the viral genetic material and put it in the envelopes.

What is the cold virus?

Usually (and in the case of the cold and flu viruses) this process repeats itself until the cell is overflowing with viruses. Then it bursts wide open like a toxic pinata and unleashes all those virus particles on its neighboring cells, and the process begins again.

Both the cold and flu viruses enter through your respiratory system, and they affect the cells lining the walls of your respiratory tract. Starting from your nose, your throat, and in many cases down to your lungs. This is why you feel your throat to be sore. Particularly 12-24 hours before the more evident symptoms start showing you might start feeling like your throat is dry and itchy, your nose feeling wet, and your mouth's ceiling/ear canals feeling itchy. That's all due to the first cells there bursting open with the virus, infecting nearby cells and your immune system being immediately put on alert.

How does your body figure out you have an intruder?

Like many others mentioned, most of your symptoms are caused by your body trying to fight the intruder. But how does your body figure out there's an intruder in the first place?

Your immune system doesn't have eyes or ears or even an actual consciousness. It does its job through complicated chemical processes. And the way to recognize an intruder is sort of what ants do to recognize each other. They touch antennae. All cells have unique proteins on their surface can be "touched" by other cells, and figure out what kind of cell this is, what job it has, what's it supposed to do now, what's its internal condition, and whether it's friend or foe. These proteins might not necessarily be there for recognition, but can be unique enough to be used for recognition anyway. So the way for your immune system to recognize intruders is to "touch antennae" with other cells, and if the proteins don't match anything the immune system knows belongs to its body, then it flags it as an intruder (that's how auto-immune disorders happen, the immune system doesn't recognize its own proteins and thinks its own cells are intruders).

As you may have figured out, there's a problem with viruses. They are hijacking your own cells. So when your body detects intruders, it's actually flagging your own infected cells as intruders. And guess what, that's where all the fun begins (well not for you right now).

Why this is not fun for you

When the body detects a serious intruder it goes into an alert. It's similar to how you get an adrenaline rush when you are in a danger (it's actually the same organs causing it, the adrenal glands). Imagine that your immune system consists of Cops, Emergency Personnel and the National Guard. Well, for all these corps to work, there needs to be a signal that calls them to action. We'll go through each thing your body does as part of the alert:

  • Fever: The increase in temperature causes your whole immune system to work better. It's like an alarm goes off and all the firemen start rushing out.
  • Inflammation: When the cops (white cells on patrol) first find out that virus particles have infiltrated your cells, they immediately go to work and start destroying as many infected cells and particles they can find. At the same time they release a signal which causes the area to swell up and will eventually cause fever. This swelling up speeds up the transfer of reinforcements of Emergency Personel (macrophage white cells - the ones that EAT intruders) and blocks off the escape of intruders into a different area.
  • Phlegm & Mucus: This is another part of the immune alert. Your cells on the respiratory tract produce more phlegm and mucus to help the movement of your cops and emergency personel, to trap intruders trying to escape and force them out, and also to clean up. This conflict isn't "bloodless". The casualties are piling up on both sides, and someone needs to get rid of all the carcasses of the dead cells. This is facilitated by phlegm and mucus. It's partly why they are so much more dense when you are sick than normal.
  • Weakness: Your body can't have you going out and about and wasting energy on useless stuff like solving math problems, lifting weights or feeding your cat. It has a war to fight damn it, and you'll contribute all your energy to it. It's also part of the alert. Your other bodily functions start shutting down. Some can't work because of the fever and inflammation, others are just not important right now. Your body is considering your situation an emergency. Also, the virus might be interfering with their normal functions (although, not so much in a usual case of cold virus). When the fever goes away, then your body will resume normal operations.
  • Bones hurting mildly: That's partly the fever, and partly the body trying to produce white blood cells. Bone marrow is where all the blood cells are produced, and it swells up slightly during disease to produce more white blood cells.
  • Sleepiness: See weakness. Your body is trying to dedicate all its resources to removing the intruder.
  • EDIT: Feeling cold and shivers: This is your body trying to increase the fever even more. The current fever is deemed not enough, and so the reaction is pumped up. As a side-effect you are imagining that you are feeling cold, even though you actually are burning up.

Why is this kind of infection so bad compared to other infections like, a skin rash?

Because by the time your body realizes you are under attack from a virus, it is already late enough. A skin rash is an early alert, that is executed in a timely and disciplined manner. The alert doesn't even go all the way, your Emergency Personnel are usually enough to take care of it. But when a cold is detected, it's usually when enough viruses have already replicated (incubation period) and are performing a massive attack on your body. Your infected cells are bursting simultaneously and in large numbers, infecting even more cells. Your body is in a panic, because the situation is actually quite serious. The enemy can not be allowed to spread further, particularly to somewhere as important as your lungs.

It takes so long for your body to get rid of a cold, because it has already taken it long to figure out it's being invaded by a virus. Your body is trying to formulate antibodies (the National Guard response), that will go find all your infected cells and put a hit on them. I mean a literal hit. Some white cells we call White Killer Cells come along, find all the marked infected cells and induce apoptosis, i.e. they cause them to kill themselves, and therefore stop the invasion.

Once you start feeling better, is when your body has finally beaten the virus. The fever, sleepiness, weakness, inflammation, phlegm and mucus persist until the area has been cleared and your body makes sure that no more virus particles are around.

How do I avoid catching a cold?

Contrary to popular belief you don't catch a cold just because you went out in cold weather, or you were sweating and some wind happened to blow at that time, or you were walking around barefoot on the cold floor. It's silly when you think about it. How can cold temperature produce a virus out of thin air in the first place?

The cold (and flu) virus are flying all around us, and really like snuggling in our respiratory tract. They are usually in inactive form. Meaning they are just waiting for the right conditions to start reproducing, by invading your body and hijacking your cells. Every time you come in contact with another human, it's likely you'll exchange virus particles. But they are inactive, so it's fine.

However, the virus particles will activate if there's a significant drop in temperature. Particularly at 30-32 C (body normal is 36-37 C), is the perfect temperature for their proteins to start acting up and invade living cells of a host organism. This is why you are more prone to catch a cold if you are feeling cold. Inhaling the cold air in your environment will drop the temperature in your respiratory tract and cause the virus particles to activate.

Winter is a nasty period for cold, not just because of the weather, but because we tend to all stay inside with other humans. More contact and breathing the same air over and over, maximizes the chances that you get some virus particles residing in your respiratory tract, waiting for a chance to strike.

So, you need to make sure you are somewhere warm, make sure you air the rooms you occupy whenever the outside weather allows, change environments, avoid packed rooms, and always cover up your chest, neck and mouth/nose with warm clothing. Take these precautions and you'll minimize your chances of catching a cold.

If anyone's interested, original answer was posted on this thread and was the top answer, but it's deleted now : https://www.reddit.com/r/askscience/comments/7innjm/what_exactly_does_the_cold_virus_do_to_me_to_make/