I think this is a good addendum to OP with tips and details that aren’t so obvious and may save folks some time.
I can distill a decent chunk of the trouble free pool method down to a couple steps and key knowledge points. Fixing and maintaining a pool isn’t without its costs but hopefully this can get things going in the right direction without spending a ton of money.
First, know your pool specs. Gallons, salt or fresh water, pool age, type (plaster/fiberglass/liner), above or in-ground, what you use for sanitation (chlorine and what type, bromine, etc) and type of filtration (cartridges, diatomaceous earth, etc).
Then know all of your test readings. Free chlorine, combined chlorine, total alkalinity, pH, and cyanuric acid for starters. Then calcium hardness, salt level and borates (if a salt water pool). There’s some debate about whether or not you should use your own testing versus pool store results. https://www.troublefreepool.com/blog/what-are-my-ideal-pool-levels/
I fall into the camp that you should do your own testing. Avoid test strips…they aren’t accurate or reliable enough. The #1 priority is to have a good water test kit. I use the Taylor K-2006C water test kit with a SmartStir and a Taylor SampleSizer. Makes it almost brainless to do the periodic chem checks with a high degree of accuracy and consistency.
Once we have all of your test results, only then can we start talking about what to do with your pool. For example the problem could be not enough chlorine, too much cyanuric acid, or a combination of factors. To clear up your cloudy and green pool, you’ll want to start with a SLAM. https://www.troublefreepool.com/blog/2018/12/12/slam-shock-level-and-maintain/
As far as what Chemicals to use to balance your pool, here's my list. They're cheap, pure, relatively available in most places, and can generally fine tune one test result without messing with the others. While this might seem like a lot, most of these are used only once or twice a season (if at all). They also result in a very low maintenance pool that can be tested once a week or less. I test FC, CC, pH and Alkalinity weekly. CH, CYA, Borates, and Salt monthly.
CHLORINE (TC/FC/CC): SALT WATER CHLORINE GENERATOR PREFERRED. OTHERWISE USE LIQUID CHLORINE (EVEN WITH A SWCG THIS IS NECESSARY WHEN TEMPS ARE LOW ENOUGH THAT YOUR SALT WATER CHLORINE GENERATOR CAN'T FUNCTION (BELOW ABOUT 60 DEG F): https://www.homedepot.com/p/HDX-128-oz-Chlorinating-Liquid-3-Pack-30128HDX/303115700
PH/ALKALINITY REDUCER: https://www.homedepot.com/p/HDX-1-Gal-Muriatic-Acid-2-Pack-pH-Adjuster-10031HDX/100344765
PH INCREASER (probably won't need this much): Borax or Soda Ash. Soda Ash is purer. You can also use aeration instead by running your pool pump longer to increase pH. https://www.dudadiesel.com/choose_item.php?id=sc50&gclid=Cj0KCQjw38-DBhDpARIsADJ3kjn6tibmQI3vXXk-hw-QO5lPfBXe0yLOuAC0yAPx5GwcWvZhuYMFNuIaAktCEALw_wcB
ALKALINITY (TA) REDUCER: https://www.homedepot.com/p/HDX-1-Gal-Muriatic-Acid-2-Pack-pH-Adjuster-10031HDX/100344765
ALKALINITY (TA) INCREASER: https://www.amazon.com/Arm-Hammer-Baking-Soda-16/dp/B000PYF8VM/ref=sr_1_5_0o_fs?dchild=1&keywords=BAKING+SODA&qid=1617131310&sr=8-5
CALCIUM HARDNESS (CH) INCREASER: Snow Joe MELT20CPP 20-Pound 94% Pure Calcium Chloride Ice Melt Pellets https://www.amazon.com/dp/B07Z4G1LTD/ref=cm_sw_r_awdo_7JN6J31R2FWZ6AB3QTY8
CALCIUM HARDNESS REDUCER: like cyanuric acid the most reliable method for lowering calcium hardness is to partially drain and refill the pool and repeat until the readings are in an acceptable range. I’ll add that you should test your tap/well water to see if it’s a source of the problem.
BORATE INCREASER (IMPORTANT FOR CONTROLLING PH RISE IN SALT POOLS): https://www.dudadiesel.com/choose_item.php?id=boric5f
CYANURIC ACID REDUCER: CYA can only be lowered by draining and refilling some or all of your pool water. Some folks have used a chemical reducer, but the reviews are mixed as to how well it works and it’s expensive if you have a big adjustment to make.
If you don't have a salt water chlorine generator (SWCG), I encourage having one installed. It resolves the #1 PITA when it comes to maintaining a pool....adding chlorine. Long term, I think you'll agree that dirt, leaves, and debris are a bigger maintenance concern than the chemicals and testing. Two things that help immensely are a surface robot... https://solar-breeze.com/ and a robotic cool cleaner... https://maytronicsus.com/ No, these aren't cheap, but they make the pool experience much more enjoyable. Use socks with your skimmer baskets to reduce clogging of your main filter and pump with fine debris.
Finally, troublefreepool.com is an awesome resource. I recommend you use the PoolMath app. The App is very useful as it takes your test kit results and recommends chemical additions and specific amounts to correct any imbalances, and uses the chemicals I listed. They also have a terrific forum of fellow pool owners and a useful history to search. The mods are also very responsive. Here's a video on what the PoolMath app is and how it works. Start at 5:30 to skip the setup instructions.
Skip the pool stores and learn your pool. Your approach is likely going to be hella expensive over time, and will likely have undesirable side effects like CYA buildup. You also shouldn’t need things like algaecide if you keep up with your regular maintenance and test your pool weekly.
I can distill a decent chunk of the trouble free pool method down to a couple steps that you should take right now. Fixing and maintaining a pool isn’t without its costs but hopefully this can get you in the right direction without spending a ton of money. As others have suggested, starting with the Pool School is the best place to start.
First give us all your pool specs. Gallons, salt or fresh water, pool age, type (plaster/fiberglass/liner), above or in-ground, what you use for sanitation (chlorine and what type, bromine, etc)
There’s some debate about whether or not you should use your own testing versus pool store results. https://www.troublefreepool.com/blog/what-are-my-ideal-pool-levels/
I fall into the camp that says you should do your own testing. Avoid test strips…they aren’t accurate or reliable enough. The #1 priority is to have a good water test kit. I use and highly recommend the Taylor K-2006C water test kit with a SmartStir and a Taylor SampleSizer. Makes it almost brainless to do the periodic chem checks with a high degree of accuracy and consistency. Here’s how to use it, and a link to get one.
Once we have all of your test results, only then can we start talking about what to do with your pool. If you have visible algae, a SLAM may be in order: https://www.troublefreepool.com/blog/2018/12/12/slam-shock-level-and-maintain/
As far as what Chemicals to use to balance your pool, here's my list. They're cheap, pure, relatively available in most places, and can generally fine tune one test result without messing with the others. While this might seem like a lot, most of these are used only once or twice a season (if at all). They also result in a very low maintenance pool that can be tested once a week or less. I test FC, CC, pH and Alkalinity weekly. CH, CYA, Borates, and Salt monthly.
CHLORINE (TC/FC/CC): SALT WATER CHLORINE GENERATOR PREFERRED ASSUMING YOUR POOL IS COMPATIBLE (I e no aluminum, automatic pool covers, or other materials negatively impacted by salt water). OTHERWISE USE LIQUID CHLORINE (EVEN WITH A SWCG THIS IS NECESSARY WHEN TEMPS ARE LOW ENOUGH THAT YOUR SALT WATER CHLORINE GENERATOR CAN'T FUNCTION (BELOW ABOUT 60 DEG F): https://www.homedepot.com/p/HDX-128-oz-Chlorinating-Liquid-3-Pack-30128HDX/303115700
PH/ALKALINITY REDUCER: https://www.homedepot.com/p/HDX-1-Gal-Muriatic-Acid-2-Pack-pH-Adjuster-10031HDX/100344765
PH INCREASER (probably won't need this much): Borax or Soda Ash. Soda Ash is purer. You can also use aeration instead by running your pool pump longer to increase pH. https://www.dudadiesel.com/choose_item.php?id=sc50&gclid=Cj0KCQjw38-DBhDpARIsADJ3kjn6tibmQI3vXXk-hw-QO5lPfBXe0yLOuAC0yAPx5GwcWvZhuYMFNuIaAktCEALw_wcB
ALKALINITY (TA) REDUCER: https://www.homedepot.com/p/HDX-1-Gal-Muriatic-Acid-2-Pack-pH-Adjuster-10031HDX/100344765
ALKALINITY (TA) INCREASER: https://www.amazon.com/Arm-Hammer-Baking-Soda-16/dp/B000PYF8VM/ref=sr_1_5_0o_fs?dchild=1&keywords=BAKING+SODA&qid=1617131310&sr=8-5
CALCIUM HARDNESS (CH) INCREASER: Snow Joe MELT20CPP 20-Pound 94% Pure Calcium Chloride Ice Melt Pellets https://www.amazon.com/dp/B07Z4G1LTD/ref=cm_sw_r_awdo_7JN6J31R2FWZ6AB3QTY8
CALCIUM HARDNESS REDUCER: like cyanuric acid thr most reliable method for lowering calcium hardness is to partially drain and refill the pool and repeat until the readings are in an acceptable range. I’ll add that you should test your tap/well water to see if it’s a source of the problem.
BORATE INCREASER (IMPORTANT FOR CONTROLLING PH RISE IN SALT POOLS): https://www.dudadiesel.com/choose_item.php?id=boric5f
CYANURIC ACID REDUCER: CYA can only be lowered by draining and refilling some or all of your pool water. Some folks have used a chemical reducer, but the reviews are mixed as to how well it works and it’s expensive if you have a big adjustment to make.
If you don't have a salt water chlorine generator (SWCG), I encourage having one installed. It resolves the #1 PITA when it comes to maintaining a pool....adding chlorine. Just make sure you don’t have any corrosion sensitive items like automatic pool covers (most pools are salt compatible). Long term, I think you'll agree that dirt, leaves, and debris are a bigger maintenance concern than the chemicals and testing. Two things that help immensely are a surface robot... Betta SE (2023 Model) - Solar Powered Automatic Robotic Pool Skimmer with Enhanced Core Durability and Re-Engineered Twin Salt Chlorine Tolerant Motors (White) https://a.co/d/bikyjkL and a robotic cool cleaner... https://maytronicsus.com/ No, these aren't cheap, but they make the pool experience much more enjoyable. Use socks with your skimmer baskets to reduce clogging of your main filter and pump with fine debris.
Finally, troublefreepool.com is an awesome resource. I recommend you use the PoolMath app. The App is very useful as it takes your test kit results and recommends chemical additions from the list of chemicals I provided above, and gives the specific amounts to correct any imbalances. They also have a terrific forum of fellow pool owners and a useful history to search. The mods are also very responsive. Here's a video on what the PoolMath app is and how it works. Start at 5:30 to skip the setup instructions.