How a Virus Infects You
Viruses lie around our environment all of the time just waiting for a host cell to come along. They can enter us through the nose, mouth or breaks in the skin (see How the Immune System Works for details). Once inside, they find a host cell to infect. For example, cold and flu viruses will attack cells that line the respiratory or digestive tracts. The human immunodeficiency virus (HIV), which causes AIDS, attacks the T-cells of the immune system.

In the lytic cycle, the virus reproduces itself using the host cell's chemical machinery. The red spiral lines in the drawing indicate the virus's genetic material. The orange portion is the outer shell that protects it.

Regardless of the type of host cell, all viruses follow the same basic steps in what is known as the lytic cycle (see figure above): 

A virus particle attaches to a host cell. 
The particle releases its genetic instructions into the host cell. 
The injected genetic material recruits the host cell's enzymes. 
The enzymes make parts for more new virus particles. 
The new particles assemble the parts into new viruses. 
The new particles break free from the host cell. 
All viruses have some type of protein on the outside coat or envelope that "feels" or "recognizes" the proper host cell(s). This protein attaches the virus to the membrane of the host cell. Some enveloped viruses can dissolve right through the cell membrane of the host because both the virus envelope and the cell membrane are made of lipids. 
Those viruses that do not enter the cell must inject their contents (genetic instructions, enzymes) into the host cell. Those viruses that dissolve into a cell simply release their contents once inside the host. In either case, the results are the same. 

On the Inside

Once inside the cell, the viral enzymes take over those enzymes of the host cell and begin making copies of the viral genetic instructions and new viral proteins using the virus's genetic instructions and the cell's enzyme machinery (see How Cells Work for details on the machinery). The new copies of the viral genetic instructions are packaged inside the new protein coats to make new viruses. 
Once the new viruses are made, they leave the host cell in one of two ways: 

They break the host cell open (lysis) and destroy the host cell. 
They pinch out from the cell membrane and break away (budding) with a piece of the cell membrane surrounding them. This is how enveloped viruses leave the cell. In this way, the host cell is not destroyed. 
Once free from the host cell, the new viruses can attack other cells. Because one virus can reproduce thousands of new viruses, viral infections can spread quickly throughout the body. 
The sequence of events that occurs when you come down with the flu or a cold is a good demonstration of how a virus works: 

An infected person sneezes near you. 
You inhale the virus particle, and it attaches to cells lining the sinuses in your nose. 
The virus attacks the cells lining the sinuses and rapidly reproduces new viruses. 
The host cells break, and new viruses spread into your bloodstream and also into your lungs. Because you have lost cells lining your sinuses, fluid can flow into your nasal passages and give you a runny nose. 
Viruses in the fluid that drips down your throat attack the cells lining your throat and give you a sore throat. 
Viruses in your bloodstream can attack muscle cells and cause you to have muscle aches. 
Your immune system responds to the infection, and in the process of fighting, it produces chemicals called pyrogens that cause your body temperature to increase. This fever actually helps you to fight the infection by slowing down the rate of viral reproduction, because most of your body's chemical reactions have an optimal temperature of 98.6 degrees Fahrenheit (37 degrees Celsius). If your temperature rises slightly above this, the reactions slow down. This immune response continues until the viruses are eliminated from your body. However, if you sneeze, you can spread thousands of new viruses into the environment to await another host.