Assume I have a server running. How do it setup my own sms gateway (in Singapore)? Is there any free method? Must I buy a dedicated sms gateway or a software to run on my server?

There is quite a big difference between an "sms gateway" and and an "sms service".

An sms gateway is another name for a company which maintains its own smsc (sms centre) and aggregates connections to network operators and other sms centres using messaging protocols such as smpp.

Many companies can present themselves as an sms gateway because, at the end of the day, its very difficult to know what the real world status of an online company is.

If you want to run a proper gateway, you will need to either buy or develop a text-messaging server that acts like a mail server (which can manage mobile originated and mobile terminated sms). You also need to set up connections for sending and receiving. With regards to receiving, you would also need to lease numbers to receive sms through (most commonly... short coes).

If you just want to provide an sms service, similar to smsdome, you will still have to do the same as above but not go too deep into it. Basic technologies like PHP & MySql would be sufficient. You can then resell the connectivity that companies like smsdome provide.

I think you should get in contact with smsdome and ask them if they can give you preferential rates as you would like to resell their services. If so, that's half the job done and they should give you an API that will allow you to connect. Then, the only thing left is to connect to their API.