Hi there MI5
Apologies if you don't want to start way out at the general picture level but I'll share the overviews I've seen so that it might save the experts time typing it and they could get more detailed about the individual things!
First of all its good to know that CO2 is all about the delivery of just one more -nutrient- to the plants, just like the nutrients in other fertilizers. The nutrient it delivers is "C" Carbon and as in so many other organic things, carbon is the skeleton, like the tinker-toy or building block for organc molecules, sugars in this case. The plant uses the carbon to build glucose, which it uses to transport energy to the cells. So lots more C is needed by the plant than, say, a trace metal in a fertilizer.
The 3 current ways (that I keep seeing) of delivering this "C" to the plant are:
1) Pressurized CO2
2) DIY CO2
3) Liquid Carbon products
These each have strengths/weaknesses and tradeoffs. Cutting through all the stuff I'm about to say, I'd judge Pressurized as the best, DIY next and Liquid Carbon third, but plenty of aspects are blurred, especially between the last two general types I suppose.
Pressurized often has the largest up-front cost, unless you take measures to do a lot of build it youself effort. After this large up-front effort/cost though, it is more reliable and easier and cheaper to maintain than the other methods. I believe a large tank can last a long time (a year?) and the tank should last forever. You need to learn about regulators, drop-checkers, bubble-counters, pH, reactors, diffusers and special tubing. Hopefully the experts will come along and describe the costs etc.
DIY do it yourself is the category of producing CO2 from fermenting yeast. There are inexpensive kits in the LFS to make this easier or you can construct these out of two liter soda bottles, put in sugar and yeast and run a CO2 line to a diffuser that bubbles CO2 into the aquarium. The problem with these is that they take more watching and fussing with and after a while the maintenance gets to be a bother to most people.
Liquid Carbon seems to be a relatively new option (when did this come on?) with the two product examples being EasyCarbo and Seachem Flourish Excel. The chemists at these companies say they have designed organic carbon molecules that can be taken in by the plant and used at some stage in the plant's glucose production process. The problem here is that you are tied to buying a relatively expensive bottled product on and on. These products also behave in significantly different ways than CO2 from the two previous methods, so you have to study up about it. They have the potential both to get rid of some algaes and also to "melt" certain types of plants when introduced, so its complicated. These products also have some utility when used simultaneously with CO2 (but I forget what!)
OK, you probably already knew all this and didn't need another beginners yakking

but maybe some tidbit in there might have interested you.
~~waterdrop~~