I used to do it religiously. I even had a special chain cleaner like this:
I'm a bit slacker now and mostly just wipe it down with a kerosene soaked rag, dry it and apply some chain lube from a bike shop:
For a while I used WD40, which relatively cheap and easy to find, but washes off quickly.
If the chain has been neglected for a while and gotten rusty I take it off, and scrub the rust off with a wire brush, rinse in kero, lube and put back.
You need a chain breaker to do that:
In Australia I used to use an automotive degreaser to clean the chain, which was very cheap and effective, but I haven't found this in HK. It's not easy to even find kero. Doesn't seem to be any for sale on Lamma (anyone seen it?), but I found it in old-fashioned rice and dry goods shops, sold as a cooking fuel. You can use turpentine, but that will degrade any plastics, (eg, it will destroy toothbrushes if you use an old one to brush the chain) also it's not oily like kero.
It helps to have long mudguards, not only protects you but you get a lot less grit and mud on the chain when it's wet.
Frequency is variable. You really should give it a wipe down (run the chain through a rag in your hand) and reapply the lube every time it gets in the rain. This time of year, once or twice a month is enough.
You also need to clean the gear cluster (brush, pull a rag between the gears and wipe down) and the derailleur (clean the gunk off the jockey wheels, lube).