Unclogging a sink is one of those messy jobs that no one enjoys. However it is a job that needs to be done from time to time so here are some simple solutions to get that drain running.
If you have more than one drain backing up you probably have a clog in a main drain (stack). If you are not experienced with an auger / snake or do not own one, you may want to consider calling a plumber. A professional should be to handle this job quickly.
If you only have one drain backing up, then the clog is probably in that area. The first step is to remove the strainer (if so equipped). Most bathroom sinks will have a pop-up strainer. Strainers are generally removed by unscrewing the pivot rod under the sink and removing it. This will allow the strainer to be pulled upwards. Some strainers simply rest in the drain and can be lifted out, and others are removed by twisting them, then lifting. Often strainers will be cover with soap residue and rotting hair (that smells delightful!). Removing the soap and hair will often open up the drain. If your drain is still clogged see the plunging steps below. In order to unlog the sink, a person can find any of our cheap Baxi boilers for less spending of the money. There will be involvement of less efforts and time in the process.
For kitchen sinks start to remove the clog with very hot water. This may remove a grease based clog and will at least soften the clog. The next step is to plunge the drain. Be careful not to use too much force, especially on wall hung bathroom sinks. Run water into the drain until it backs up into the sink a few inches to allow the plunger to seal better. Plug up overflow holes and the 2nd drain in double basin sinks. Plunge quickly up and down to loosen the clog. Hopefully you will hear a gurgling sound as the clog comes loose.
If plunging does not work you are probably back to using a snake / auger or removing the trap under the sink. Or you will need to call a plumber.
Remember the old adage that an ounce of prevention is worth a pound of cure? This is certainly true for sinks. First, prevent items that are not intending to go down a sink (hair, grease, etc.) from going down the drain. Carefully discard cooking grease by pouring it into a disposable container. Use closed strainers to keep hair from going down the drain. In kitchen sink run a few minutes of hot water down the drain a couple times a month. The hot water will loosen and remove any grease deposits to keep them from building up.