No real plumbing issue can be solved with duct tape or other temporary measures. However, in a pinch, you can patch together a quick fix that will hold until the plumber arrives or until you can get the proper parts from the hardware section at the local discount store. You can use items you have around the house to tide you over.
If you don't have several rolls of duct tape around your house, you are living without one of life's best and cheapest fix-alls. Duct tape can cover rips in your dining room chair upholstery, your kid's gym shoes, and even the inside rip in your winter coat. This fix-all is also perfect for stopping or at least slowing the leak in pipes. You will need to turn off the water, dry the leaking area, and then tightly bind the tape around the leak. Ideally, you should only use the tape for a short period of time. It will not work for days or weeks, but you might get by for a day or two.
If your toilet is running constantly, it may be because the ballcock is never reaching the level it needs to in order to shut off the water. You might need to replace this item down the line, but in the short term, you can try and bend the rod downward slightly. That way, it will trigger the water to shut off sooner and not continually run into the flush valve. You need to be gentle, or you will end up breaking the rod. This action may tide you over until you can have the faulty parts replaced.
The drip, drip, drip of a leaking faucet can drive you close to madness, particularly in the middle of the night. Fortunately, you can temporarily mitigate this problem by using an easy trick. Simply placing a container under the leak doesn't work because you can still hear the water hit the bottom. However, if you place a sponge in the container, you shouldn't hear a thing. You still need to get the leak fixed, but you won't go crazy in the meantime.
These fixes are temporary ones, so don't postpone having these issues fixed for weeks or months. You'll lose water and maybe incur bigger problems. However, using these methods can tide you over until the plumber arrives or you don your own DIY mantle. Visit sites like http://www.firstclassplumbinginc.com to start looking at plumbers in your area.