Sitcoms hire many unknown actors and some lucky enough to be cast in hit sitcoms actually become stars. To be hired onto a sitcom actors usually have to have some experience and an agent. Sitcoms rarely hold open casting calls and normally the production companies turn to agents to help with scheduling auditions for the new show.
Most new sitcoms start out with a pilot episode. The pilot is then shown to networks and if the network likes the pilot, the sitcom may then become a series. Many pilots never make it onto the small screen but the ones that do help the actors involved build their careers.
Many pilots get cast every year. These are shows that no one has heard of yet, it if successful, the show can go on shooting for many years.
Auditions for pilots are handled through agents and the casting directors usually have some specifications in mind when they ask the agents for actors. If you have a good agent and you fit the specs then you may get scheduled for a sitcom audition.
Another way to get into sitcoms is by being an extra. Now, you will not get any fame this way but you will get some experience on set. Becoming an extra is fairly easy and you can look at becoming an extra for more information about it.
Some sitcoms add and replace characters as actors leave or the writers change things around. To get onto an existing sitcom, well, you still need an agent because those do not normally go out as open calls to the general public.
There is a reason that casting directors use agents. That reason is that casting directors have little time to deal with inexperienced actors and need the agent to thin the field for them. They do not want to look at 1000 people 999 of them who may not fit the bill. They would rather look at a few who are perfect and make a decision that way.
If you want to be in a sitcom, well you better go find an agent and hopefully luck will be on your side.