The sink itself should be cleaned as you would any other surface made of that material – ie, use a stainless steel cleaner for steel sinks etc. As the sink gets a lot of use, it's also a good idea to fill it with water and whatever cleaning agent is recommended, put the plug in and leave to soak for an hour now and then.
To clean the drain, pour 4 litres warm water down the sink mixed with 200g thin bleach. Let it drain and then rinse with warm water.
Keep a plunger handy to loosen blockages in the sink. Unblocking drains from the outside is a horrible job – try to avoid blocking by scraping pots etc into a sink-tidy before pouring anything down the sink, and don't throw tea leaves and coffee grounds down it – they will cause blockages.
You have to be more specific. Is it a stainless steel sink? A porcelain sink?. Or a cultured marble sink?