When assembling DNAs via the classical restriction-ligation method, cohesive "sticky" ends / overhangs are first generated by digesting DNA(s) with a restriction endonuclease, followed by the digested products being joined together via the overhangs in a ligation reaction, where DNA ligase, usually the highly active one from T4 bacteriophage, ligates DNA, coupling ATP hydrolysis with the formation of phosphodiester bonds between overhangs that dynamically anneal based on DNA base-pairing thermodynamics.
Heat inactivation or gel/column purification of digested DNAs are typically required to prevent restriction activity from acting on other DNA fragments in the ligation, but it may be optional if no restriction site is reformed in or present elsewhere in the intended product, just as in a typical Golden Gate assembly.
If the cohesive ends are symmetric, consider the different orientations ligated products can form. Ligation products are generally used to transform bacteria, so only selectable plasmid replicons need be considered among all ligation products.
Some thermophilic DNA polymerases leave 3' adenosines, which can serve as sticky ends for simple, nondirectional assembly. Blunt ended DNAs can also be ligated, usually with a crowding agent such as PEG and/or longer, lower-temperature reaction time.
Read more: DNA Ligation | NEB
Ligations are set up like Golden Gate assemblies but without the endonuclease. For ligations with cohesive ends, 15–10 min reaction time at room temperature is common, followed by heat inactivation and transformation or freezing.