1. A medium or large refiner. The more the merrier as it will only increase your total yield. You can learn these by doing the Base Computer tutorial quests or buy them directly at the Anomaly with Salvaged Data. You can set up multiple refiners but they will need to be spread out. You can have 3 medium refiners and 2 large refiners in a local area although if you move far enough away (about 15 yards or 40-45 units) and you can place even more. See below for more info.

2. Oxygen. You can buy this in decent quantities at space stations from the Galactic Trade Terminals or from pilots that land at the station although this is a finite source but it does replenish over time (about 3 hours I believe). You can get about 3,000+ oxygen per named individual seller. You can also get it from some hazardous flora in caves and from the red Oxygen Rich Plants you can find on the surface of most planets/moons. It can also be found in some flora and minerals but in low amounts, you will also need an Analysis Visor to gain access to secondary materials from those sources. I recommend buying it from the pilots at space stations since you can get the most at once per purchase. Sidenote: If you need to make some units to get this started, simply go to any planet with caves and mine some cobalt or gather the special resources found on that planet such as Albumen Pearls, etc. These special resources appear with a tier indicator of " III " above them when viewed with the Analysis Visor. You can also use this refining method with cobalt or refine cobalt to create ionised cobalt just in case you already have a decent amount of oxygen but need more units.
2 cobalt + 2 oxygen = 5 ionised cobalt, or 1 ionised cobalt + 2 oxygen = 6 ionised cobalt.

https://nomanssky.gamepedia.com/Oxygen
https://nomanssky.gamepedia.com/Cobalt

3. Chlorine. You can find chlorine as a resource node that you can mine with the Terrain Manipulator, from certain flora and minerals, from trade terminals, pilots, and also from refining certain materials. Salt is the best source to refine from because you can find it easily and if you combine 2 salt with 2 oxygen in a medium or large refiner you will get 5 chlorine. I recommend buying or foraging for just a small amount of salt then using this refining method.

https://nomanssky.gamepedia.com/Chlorine

4. A location to get this party started! I use my freighter because it has all of my storage and plenty of room for multiple refiners. If you use your freighter for this method, plan accordingly as space is limited as opposed to an open world base where space is also limited but it is an open space and not confined like on a freighter. I use a combination of about 25 medium and large refiners spread out across my freighter. If you create a large room that is at least 5x5, you can place 3M/2L refiners in the corners. Sidenote: There is a glitch with freighters that if you warp them anywhere there is a chance you could lose everything in refiners that are aboard your freighter. Just be sure to empty your refiners before warping your freighter and hopefully you should have no problems. I've heard that this is actually an intended feature but I couldn't find any direct confirmation from Hello Games.

There isn't much to it. Simply add oxygen and chlorine to a medium or large refiner to create even more chlorine at an increased ratio. 1 chlorine + 2 oxygen will create 6 chlorine. You will be able to create up to 4095 Chlorine per refiner then simply move that stack to the input section and keep producing chlorine based on how much oxygen you have. It takes 4:05 per stack size of 4095 and a full stack of 9999 in Normal mode is valued at about 6,000,000 units. Take those units and buy even more oxygen from pilots at various space stations to keep the process going.

Congratulations! You are now well on your way to becoming a billionaire, and all without cheating, using exploits, or relying on handouts from other players. Enjoy and happy journeys fellow travelers!

Props to gamepedia for having such a great database for this game!