Viruses are absolutely amazing. Although they are not themselves alive, a virus can reproduce by hijacking the machinery of a living cell. The article How Viruses Work describes viruses in detail -- below is a summary.
A virus particle consists of a viral jacket wrapped around a strand of DNA or RNA. The jacket and its short strand of DNA can be extremely small -- a thousand times smaller than a bacterium. The jacket normally is studded with chemical "feelers" that can bond to the outside of a cell. Once docked, the viral DNA (or RNA, depending on the virus) is injected into the cell, leaving the jacket on the outside of the cell.
In the simplest virus, the DNA or RNA strand is now floating freely inside a cell. RNA polymerase transcribes the DNA strand, and ribosomes create the enzymes that the viral DNA specifies. The enzymes that the viral DNA creates are able to create new viral jackets and other components of the virus. In simple viruses, the jackets then self-assemble around replicated DNA strands. Eventually the cell is so full of new viral particles that the cell bursts, freeing the particles to attack new cells. Using this system, the speed at which a virus can reproduce and infect other cells is amazing.
In most cases, the immune system produces antibodies, which are proteins that bind to the viral particles and prevent them from attaching to new cells. The immune system can also detect infected cells by discovering cells decorated with viral jackets, and can kill infected cells.
Antibiotics have no effect on a virus because a virus is not alive. There is nothing to kill! Immunizations work by pre-infecting the body so it knows how to produce the right antibodies as soon as the virus starts reproducing.
See How the Immune System Works for further details.