There are several ways to fix a clogged drain that are eco friendly and require very few tools. It largely depends upon what the clog is as to how you should proceed.
Step One: Grease Clogs
For a grease clog first use a plunger or plumber's helper to try to loosen the clog. This may take several attempts as grease clogs are very stubborn. If the plunger doesn't work then your next step should be to remove as much water as possible from the sink by dipping it out or sucking it out with a shop vac. Once the water is removed pour about a half cup of dishwashing liquid or pine cleaner into the clogged drain. Let it sit for a couple of hours or overnight. Then boil a large pot of water and pour into the drain. It may take a while for the water and cleaner to work and you may need to assist it with the plumber's helper. Continue this treatment until the drain clears.
Another possible fix is a manual snake that you can purchase for a relatively low cost at a hardware store. Simply feed the snake wire into the drain until you feel resistance then move it around to unplug it. Flush with hot water for a few minutes.
To prevent grease clogs, routinely pour a pot of boiling water down your drain to keep it clear.
Step Two: Hair Clogs
Hair is the number one culprit of clogged bathroom drains. Generally if you remove the plug from the sink a large wad of hair will come up with it and all you need to do is remove that plug and re-connect the plug and you'll have a free running drain. If not, you will probably need to use the plumbing snake as described for the grease clog above. Snake it in until you feel resistance then remove it. Run water to see if you got it all and repeat if the drain still runs slow.
The same applies for a bathtub drain. Be sure to clean the screen covering the drain after each shower or bath to help prevent this problem.
Step Three: Toilet Clogs
The best way to clear a clogged toilet is to use the plunger or plumber's helper. Be sure to use one that has a bell end rather than a smooth ended one. A bell end plunger forms a very tight seal which produces suction. You may need to manipulate it several times to loosen the clog. Never put chemicals down into a toilet bowl to loosen a clog as it can ruin your plumbing and is not eco friendly.
Step Four: Prevention
The best way to not deal with clogged drain is prevention. Don't pour grease down your drains, not even in small amounts. The same holds true for food scraps, coffee grounds and other waste. Always run water for a while after using your garbage disposal to be sure the waste is all the way to the main sewer line.
Routinely clean hair from bathroom drains to prevent clogs.
Some people like to use a mixture of dumping baking soda down a drain, waiting a few minutes, then pouring in a cup of vinegar for a natural cleaner and deodorizer.