If you're new to the site, the first thing you should do after filling in your profile, adding a good photo and racking up some actual tweets, is to follow some good local accounts.
You can get cracking on this simply by using Twitter as a search engine, and defining the location. This will get the ball rolling.
Eventually you'll have to turn to your actual network for more accounts to follow. Because tweeps often follow businesses and individuals in their city, you just have to look at the lists of those who follow them and you'll find heaps.
A good place to start is with accounts like Tweet Perth, and Freo Cookster. They have a lot of local followers, many of whom are businesses. Another way is to find big government organizations and corporate accounts that are based in this city. Examples include Transperth and Perth Zoo.
You can flip that approach on its head and look at the lists that local business related accounts are following. An example might be Pamphlets1.
If you're in the hospitality and entertainment niches, you'll have a very long list before you know it. After all, there are an awful lot of cafes, restaurants and bars on Twitter. If you supplied this industry you'd be crazy not to join the site and get active.
You'll find that about a third of the ones you follow will follow you back. (Actually, you can see this ratio in action on this very account.)
Then you just have to get on their radar. Retweet, follow, and mention them occasionally and they're sure to see you. Gradually the followers will come. Many tweeps still look at your website, regardless of whether they end up following you. And even if they don't do that they still know your business name and what you do.
And remember that these people are usually the decision makers for those businesses. So one day when they are thinking about purchasing products and services in your niche they may well consider you. Now this wouldn't be happening if you weren't on Twitter.
Sure, you could do this on other social sites. But I think Twitter is best for this because it's so fast and direct.
I have found that posting photos on Twitter works well (as it does on all social media sites). So consistently adding them is a good idea. You'll see that the cafes and restaurants are always posting mouth-watering shots of latest creations. But you could do this in any field.
Asking questions is also recommended. Maybe post a shot of something you're fixing, then ask your following on their thoughts on whether they've had the same problem. The key is to get them replying. And you should of course reply to their replies.
Say you have a pest control business. You could ask other businesses what their most persistent problem is.
And remember: Don't sell. Just ask.
Tips are always good. They help you build authority. And people like to retweet them too. Maybe you could offer tips from a local angle. There must be many things you'd do differently in Perth's dry climate for example ...