Waste pipes are usually made of plasctic they take away the waste water to be discharged down your drainage. These can be found coming off baths, sinks and basins. These are easy to work on and require no real specialist knowledge. Joints are sealed via solvent weild (basically a glue for plastic).
If water is slow to drain away or will not drain at all then chances are one of the following is to blame.
Blockages - food and hair can collect (depending what appliance the waste is coming off) where the flow of water slows down. To remedy this you need to remove the blockage by rodding, plunging or using a chemical blockage remover. In extreme cases you may need to replace that section of pipie with new.
Incorrect fall - the waste pipe should be constantly falling down throughout the pipework run towards the drainage point so that gravitry can take away the water. If this is causing your water not to drain away properly then it needs to be altered. To do this you will need to alter the pipie clips so the pipiework is falling the right way. In extreme cases you may need to renew the pipe.