Hello
In order to insert a gene into a plasmic, you must covalently connect the sugar backbone of the two DNA fragments. This reaction, called ligation, is performed by the T4 DNA ligase enzyme. The DNA ligase catalyzes the formation of covalent phosphodiester linkages, which permanently join the nucleotides together. After ligation, the insert DNA is physically attached to the backbone and the complete plasmid can be transformed into bacterial cells for propagation.
The majority of ligation reactions involve DNA fragments that have been generated by restriction enzyme digestion. Most restriction enzymes digest DNA asymmetrically across their recognition sequence, which results in a single stranded overhang on the digested end of the DNA fragment. The overhangs, called "sticky ends", are what allow the vector and insert to bind to each other. When the sticky ends are compatible, meaning that the overhanging base pairs on the vector and insert are complementary, the two pieces of DNA connect and ultimately are fused by the ligation reaction.
The example below depicts the ligation of two sticky ends that were generated by EcoRI digestion:
Usually, scientists select two different enzymes for adding an insert into a vector (one enzyme on the 5' end and a different enzyme on the 3' end). This ensures that the insert will be added in the correct orientation and prevents the vector from ligating to itself during the ligation process. If the sticky ends on either side of the vector are compatible with each other, the vector is much more likely to ligate to itself rather than to the desired insert. If you are in this situation, it is important to treat the digested vector backbone with a phosphatase before performing the ligation reaction (phosphatase removes the 5' phosphate and therefore prevents the ligase from being able to fuse the two ends of the vector together).
If you need a step-by-step protocol, don't be afraid to ask!