The Leaky Toilet
The flapper may be corroded or damaged, the fill valve broken or the chain is too long or short.
If the toilet flush arm chain only has one inch of extra chain, unhook it and adjust. Check the be certain the rubber flapper (connected to the toilet flush arm chain) is covering the hole where the water comes in. If it isn't, attach it firmly in place. If it is in place, unclip it and check for erosion or damage. If the flapper is damaged, it will need to be replaced.
If the water level is higher or much lower than the water level line on the inside of the toilet, you'll need to adjust the float arm. More modern toilets often have fill valves in place of the float arm. When adjusting a modern, ball-less fill valve, look for a verticl arm just off the main body of the fill valve. Either squeeze the clip, move the arm up or down or use a screwdriver to loosen or adjust the bar. When working with a float arm that has a ball, gently bend the arm to adjust it into place.
The Leaking Faucet
With time, age and use, the washer or o-ring eventually needs to be replaced.
Remove the caps on the faucet to reveal the screws and tighten the screws slightly. If the faucet is still leaking, take it apart to look for any parts that are damaged such as the washers or o-rings may need to be replaced. Replace any damaged parts with an exact replacement before reassembling the faucet with the new part(s).
The Clogged Drain
Too much matter can create a clog in the pipes.
A good plunging may solve the issue. If not, a plumbing snake may be able to break up the blockage.