Building a community website for the entire world could seem like too big of a goal for some. In which case those people should not give up on making a community completely, instead just make a local community website. Making a local community website is easier than making a community website for everyone. This is especially true if the creator of the website is from that local area that the website is for.
In order to build a local community website you could essentially follow the same path as those who build community websites for everyone, except on a smaller scale. You can create the site yourself if you feel confident in your web development and design skills, but if you do not then getting a professional web developer and designer to create the site for you is a good option. Once the site is made it is time to think of hosting, if you wish to host the site then you have to be willing to give up some of your free time so that you may monitor your server and make sure it is in good condition. You could always just pay a hosting company to host your website however. The website in general should be cheaper to host than one that would be used as a community for the whole world, since it will use less bandwidth and take up less space in the process.
Once the website is finished and successfully published onto the web you should consider advertising the website. This is where things should be a lot easier and probably just as effective if not more than advertising for community sites that are open to a larger base of people. If you live in the area that the community website is for then you can go out and advertise for the website yourself, put up flyers around the area that advertise the site, perhaps pass out some flyers to people on the streets, by doing this you will let people know about your site, and since it is for their own local area people will be even more interested in it. You may still want to make a few advertisements for the site on the web but this may not be entirely necessary, it is up to the creator of the site to choose if they wish to or not. Either way hopefully within a few days more and more users will join the community until it is up and running at full speed with tons of users every day.