To do this I've been using a tried and true method of building a network. And that is to follow people in your target demographic. Do this and a good proportion of them tend to follow you back. A good way to find these people is via the categorized lists that users make up.
You can do this for any niche. It can be good if you are looking for people in your city, particularly early in in your Twitter journey. However, you have to be careful when using this method because you look at the lists marked, say, "Perth tweeps", "Perthians", etc, you'll find that a large proportion of them that are no longer active. So you should just check when their last tweet was before following them.
In any case it is a strong reminder of just how many people do get into Twitter, go for a while, and certainly long enough to get on the radar of others. But they don't hang in there. (Perhaps some of those dormant accounts will start to stir again. They haven't been deleted after all. I'm sure the owners of many of them do intend to get around to it.)
Anyway, once you've found some good people in your target niche -- local or otherwise, if that's your focus -- you can find still more by looking at the ones they follow, and who follow them. But don't scroll down too far when doing this. You want to find the people who have joined these lists recently as opposed to a long time ago. These will be much more likely to be active for obvious reasons.
Although a big part of your motivation for following these people is the hope that they will quickly follow you back, don't make it the only one. Try and find good people that seem interesting and engaging and have solid followings. This is because regardless of whether they're following you, if you do start having conversations with them, they'll be replying to you using your handle, which will be seen by a proportion of their followers. And they may well end up following you in the long run as a result of this interaction anyway.
After a while you will find that some people just won't follow back. So it's fine to unfollow them so you can follow others and keep building your network. But if you've done it this way you're not "churning and burning" which looks very spammy to Twitter.
Speaking of which: When doing this I wouldn't follow more than twenty tweeps a day. And have a few days off from time to time. If you follow too aggressively you may end up being marked as a spammer by the site's internal algorithm and have to spend time in "Twitter Jail" (Twitmo). Needless to say you can do without that anxiety ...