Push the plunger up and down a few times in the toilet bowl so the plunger flange fills with water. Then push the open end of the plunger into the drain to create suction. Depending on its severity, you may need to apply some force and be aggressive as you force the clog out.
If the plunger isn’t getting you very far, try the closet auger. This tool is designed to clear the worst of clogs and can be found at any home store. The auger has a short drain snake (or cable) inside a metal tube that is bent on the end to aim up into the waste hole.
First, pull the handle out and insert the other end into the bowl. Fish it around the drain a few times to push the clog through. Flush the toilet while pulling the cable out, this will clean it off. A combination of the plunger and auger should fix your problem. If your toilet is still clogged, call a professional.
If your sink or bathtub drain is clogged: You can first try dry baking soda and vinegar (instead of Draino) to remove the clog. Pour ¾ cup baking soda, then ½ cup vinegar down the drain. Then, cover the drain with a rag or plug. After 30 minutes, try to pour hot water down the drain.
If this doesn’t work, unravel a metal clothes hanger and make a small hook on one end (needle nosed pliers can help with this). Put this end into the drain and push the clog out past where it is blocked using a plunger-type motion.
If this doesn’t work, you may have silverware or something larger obstructing your drain. In this case, you need a professional plumber to disassemble the pipes and find out what exactly is causing your problem!