Star Fleet ships and facilities have a supply of bulk material that is constantly recycled into needed materials and items. When a request is made at a replicator terminal, the waveguide conduit system on the ship relays a small amount of bulk material to the replicator, which uses it to create the materials called for in the pattern. The object is then beamed in to the terminal.

Some elements cannot be replicated. (The Tech Manual talks about "quantum transformational manipulation", so they can do some quantum twiddling to get new elements). However, the energy costs are high for all forms of replication, and food - since it's usually just different arrangements of the same basic things (water, proteins, lipids), is more practical to replicate from bulk matter than to store.

Once the replicated item is no longer needed, they are put back in the replicator terminal and recycled as raw materials to the bulk matter store.

In some cases the replicator is used to make various components and using a transporter-effected swapout of the damaged part, but since transporters and replicators use a lot of power many of the replicators would go off-line in Alert situations. For large scale repair it's best to have the vessel put into dock at a repar facility such as a Spacedock where the damaged componenents would be in store or could be replicated easier.

It is not possible to replicate something at the quantum level! The amount of information needed to define a living, thinking being for example, is incredibly large, far surpassing the computer capacity of any 24th century database.