Thanks so much for the feedback, I have fixed the bug =0)
Caveat: The following information is what I learned through my own reading, my own experiences, and through the PFI course I took last fall (I *highly* recommend this course, Kirk and Mandy-Rae are amazing instructors and the course is very rewarding). I am NOT an expert, and I suggest you take a course and do your own research before getting into freediving. Also, always practice "safe" freediving (don't do these tables in water without a buddy who has training in the correct safety procedures).
The goal of the exercises is to build up "tolerances". CO2 tables build up your tolerance to high levels of CO2, while O2 tables build up your tolerance to low levels of O2. Both are important. Rising levels of CO2 while doing a breath hold are what give you that "urge" to breathe. Your oxygen will be depleting, but it's actually the increased percentage of CO2 that triggers you to feel like you need to come up for air. This is why you should not "hyperventilate" before doing a dive. Hyperventilating purges the CO2 from your system, so that you don't feel like you need to breathe as early. However, you are still running out of O2, and without that high CO2 trigger you might not be able to tell when you need to surface and breathe - this can cause you to blackout.
CO2 tables can help your body to become more able to fight that urge to breathe. If you've ever tried holding your breath (and you haven't trained), you'll probably find that after even a short time, such as one minute, you really feel like you need to breathe. One minute is not a long time to go without fresh O2 - you aren't running out of air yet - but it certainly can FEEL like you are! By training with CO2 tables you can learn to subdue that urge for longer so that you can hold your breath more comfortably. CO2 tables are a set of breath holds which are all the same length, with decreasing ventilation times in between. As the ventilation time gets shorter, you have less time to "get rid" of CO2, so you go into the next hold with a higher percentage of CO2.
O2 tables help your body to learn to operate with lower levels of O2. They are also great for simulating the weird (and often annoying!) thoughts that may go through your head while doing a longer hold. O2 tables are a set of breath holds which increase in length, with ventilations in between that are of a constant length. As you do each successive hold, you have to go longer with the same amount of O2, so you are learning to work with a greater decrease in O2.
If you haven't tried tables before, I'd suggest starting at the easiest, then progress up. The table which is "right" should be HARD to complete (but not impossible). When it stops being difficult, it's time to move up to the next one. Note that you might be at a different level for the two kinds of tables (for example, you might find a CO2 #4 to be the same difficulty as an O2 #2, or vice versa, everyone is different this way). You should use the table from each set that is hardest but not impossible. You might progress quicker on one set that then other.
The preset tables are fairly standard, as far as I know. Those particular sets were the ones recommended during the PFI course.
I added in the custom tables for fun, and as a bit of practice at coding. They might be helpful if you want to try something different, or if you find yourself right in between two of the tables in one set. Like most kinds of exercise, changing things up once in a while can be beneficial.
I'd recommend doing the tables at least a couple of times a week - but not every day. They are (should be, at least) a workout, and as such you probably should not do them on a day when you are doing other heavy exercise. They also take a bit of time to complete.
My personal thoughts - I usually start with a CO2, then do the O2, and then try a long hold afterwards to see how long I can go, if I feel like it. I'm usually reeeeally relaxed by this time, and my heart rate will have significantly dropped. I find that lying down, listening to some music, and doing the tables works well for me. Also if I do them in the evenings they help me relax before going to bed (I suffer from insomnia sometimes). One warning though - if you do them IN bed, you might start to doze off - I woke up once and I was still holding my breath (hadn't passed out, it had only been about a minute, I was just really sleepy). If you are planning on using these to train for a situation where you need to fight nerves and weird thoughts, you should probably try to concentrate more on what you are feeling and how you can combat the psychological stuff that goes along with longer holds. The tables are good practice for that too!