The most common drain to get blocked is the one in the kitchen sink, although the procedure is the same for any household drain. To unblock a toilet, see this guide. Food is often rinsed off of plates and cutlery and makes its way down the plug, causing a blockage.
The most common place for the blockage is in the u bend. The u bend is designed to trap a small amount of water to form an air tight barrier between the drain and the sink so that no nasty smells make their way into your home. Large or heavy solids don’t make their way around the u bend and instead get trapped. The first sign that your drain is blocking is that water in the sink starts taking longer to drain. It is best to act as soon as this occurs.
The first step is to try and plunge the plug hole. A rubber plunger (available at most hardware stores) is forced up and down rapidly over the sink hole which in turn causes the water in the u bend to move upwards and downwards, thereby dislodging any blockages.
If you don’t succeed with a plunger then you will have to remove the u bend. Make sure to have a bucket handy to catch the water which may run out of the sink or the pipework. A rubber u bend usually has two attachment points, on directly underneath the sink and one after the u which connect to a PVC drain pipe. Firstly undo the pipe clamp underneath the sink and pull the u bend off. Use the bucket to catch any water which may drain from the sink. Next remove the second pipe clamp and gently pull the u bend from the drain. The blockage is most likely in this section. Use a piece of wire to hook any debris and pull it from the u bend. Once the blockage has been removed, reinstall the u bend and tighten the pipe clamps.
If the blockage is not in the u bend then you will have to call a plumber to check the drain line to your homes main drain.