Twitter not only gives you power to announce to the whole world what are you up to. It also gives you freedom on how to be a good conversationalist.
In order to make new friends, it is nice that you’re also interested with them. So, try to be a nice guy to everyone. Check their posts and if you find them interesting, reply. There’s no other way to befriend someone than approaching them. And here on Twitter, replying on their tweets is the nicest approach.
But be careful in replying here and there. Just reply with those tweets that are answerable. Or, give a response to clarify something on someone else’s tweet, to give your feedback or to offer a help. Don’t just reply as if you’re an automated response application. It’s a big NO! NO! to someone misinterpreting your account as a spam. So please, avoid that! Try to mix up your tweets with daily stories, then replies to your Twitter friends and also some links that you might want to share with your followers.