Restriction enzymes are used to excise the gene of interest (the insert) from the parent.  The insert is purified in order to isolate it from other DNA molecules.  A common purification method is gel isolation.  The number of copies of the gene is then amplified using polymerase chain reaction (PCR).
Simultaneously, the same restriction enzymes are used to digest (cut) the destination.  The idea behind using the same restriction enzymes is to create complementary sticky ends, which will facilitate ligation later on.  A phosphatase, commonly calf-intestinal alkaline phosphatase (CIAP), is also added to prevent self-ligation of the destination vector.  The digested destination vector is isolated/purified.
The insert and the destination vector are then mixed together with DNA ligase.  A typical molar ratio of insert genes to destination vectors is 3:1; by increasing the insert concentration, self-ligation is further decreased.  After letting the reaction mixture sit for a set amount of time at a specific temperature (dependent upon the size of the strands being ligated; for more information see DNA ligase), the insert should become successfully incorporated into the destination plasmid.