Mods depend a lot of the type of mod.

Entity model changes are relatively easy, often as simple as replacing texture and model files. This is highly dependent on the tech used to make the game and how it's packaged.

Sound files, similarly, are a file replacement job as long as nothing too funky is involved.

After this, we start to get into larger toolchains. We need tools to decode game data so it can be manipulated, tools to gain access to the game as it starts up or as it runs, and tools to use those tools to create modifications and implement them easily.

Graphics upgrade mods often use directx overrides, such as in SweetFX and Reshade. Sometimes they replace or override existing game files directly.

Bug fixes and additional functionality are where things get really interesting. At first, these are done with hacks done in the form of function overrides that can only be created after analyzing the compiled game executable. Later, tools are built that allow easier access and present game functions to other developers for easy modification.

And sometimes the difficult parts are skipped over entirely when developers include modding APIs or SDKs for public use.