Three main types of bluing.
Cold, Hot, and Rust.
Cold blue is for touch up and small parts. Paint on the solution, wait a bit, rinse off. Not that durable, may have strange colors, not very deep color. Multiple applications may not make the color darker or deeper.
Hot blue is what you see on most factory blued firearms. A series of heated tanks of solutions. Mainly bluing comes for a tanks of water with bluing salts. Not really a home job. But Brownells will sell you the complete setup with tanks, stands, chemicals, etc.
Rust bluing is a cold process, but using a different chemical process. It was used on firearms that could not take the heat. Double barrel shotguns were soldered together. Hot bluing could loosen the solder, so rust blue was used. Can look very nice. Multiple applications make the color darker and deeper. This place -
PJ's Gun and Metal Care - Radocy - sells a rust blue liquid. I have some, but have not tried it yet.
Parkerizing is a hot process, but it is a single container, one step process, so can be done at home. Used on many military firearms, it is a solution that you dilute with water, heat up, drop the part in, and let is steep. Brownells and Midway (and I am sure others) sell the chemical.