“Anti” means “against” and “biotics” means “life forms” say bacteria.

There are more than 100 types of antibiotics like penicillin, cephalosporin, erythromycin, etc. The antibiotics act on Staphylococcus, Staphylobacillus, Streptococcus, Streptobacillus, Escherichia coli, etc. to name a few.
The bacteria can be either Gram-positive or Gram-negative in nature depending on the Gram reaction.
Based on the bacteria that they act on, there are two types of antibiotics. They are:
They work on many varieties of disease-causing bacteria, say a broad or wide range of diseases. Example: Gentamicin, which acts against both Gram-positive and Gram-negative organisms.
This type of antibiotic actually works and targets a specific group of bacteria, say for example penicillin, which actually attacks and sabotages the cell wall of the microbe.

The antibiotic either kills the particular bad disease causing bacteria present in the body or inhibits the further growth or multiplication of the microorganisms. Slowly our immune system takes over and brings everything under control thus curing us off the infection.
Working time
Mostly there will be an immediate relief to the person in a matter of one or two days as soon as the antibiotic starts to work on the bacterial infection.
But in the case of bigger deadly diseases like tuberculosis, the treatment of taking antibiotic tablets would range from 4 months to even a year, but the symptoms like acute coughing would slowly diminish in a matter of less than a month or so.
Therefore, the working time actually depends on the type and the severity of the infection, the duration of the course of the drug, etc.
Antibiotics usually start working almost immediately (say,minutes of very few hours,also depending on the administration route , etc)We could say that this is valid for most medicines.But this does imply that the effects are immediately noticeable.In99.990% of cases the patients clinical situation does not change dramatically in such a short period of time and only improves gradually over,hours/days/weeks.