A couple of technical details: @Replies are tweets containing @Username as a reply to a tweet by the referred user. The praxis has actually emerged from the community and then was incorporated in the technical infrastructure of Twitter itself. By now, you can hit the "Reply" button of any tweet and it will open up a text field with the according @Username prewritten. You can read @Replies to yourself in your timeline or in the "Connect"-tab on Twitter.
Good to know: @Replies by people you follow to people you don't follow don't show up in your timeline.
Now that we have enough theory under our belt, let's come to the real problem: Before spamming everyone you follow with @Replies, you should reflect the medium you're communicating in, who the entity is you're trying to communicate with and if you have really understood the tweet you're commenting.
A Billion of Monologues
Twitter is a profoundly weird medium. It's not focused communication, it's a lot like broadcasting. Some use it as a news aggregator, some as means of self-expression and some as an advertising channel. When a dialogue is two monologues clashing, then Twitter is a billion monologues clashing. That means that usually, you do not expect a reply to your tweets, except you explicitly called for it. Even questions usually are rhetorical in nature. The only interaction you actually expect are favorites and retweets, both being a form of mere acknowledgement and minimal validation. They basically only say: I noticed it and I liked it.
Sorry to bust your bubble, but Twitter isn't only for real people. There are bots, magazines, TV stations and companies, stars, politicians and public services, all of them not likely to engage in communication initiated by regular users. Either they aren't even interested in conversing, as they are only on Twitter because their Social Media Expert told them to, or they are interacted with so much, they can't possibly respond to all of it. Or maybe their Communication Strategist never even though about the possibility of interaction and the media persona they have taken has no point of reference for the communication mode of "dialog".
My golden rule for writing and sending @Replies is: Know thy context! Tweets consist of a maximum of 140 letters. As you can imagine, this is quite the restraint for argument quality and lopsided, ambiguous, unspecific or incomprehensible statements may occur on a fairly regular basis. Here are a couple of things you should take into account before @Replying the shit out of this totally messed up opinion or that rather cryptic joke that guy just tweetet:
- When you don't get it, don't write an @Reply. Twitter is not for lengthy explanations.
- Pay close attention and closely reread the tweet. Are there several ways to read it?
- Who is the twitterer? Do they have a blog explaining their point of view or are they known for a certain topic? Can and will they probably react to your reply?
- Does the tweet follow a trope they often use?
- Are they serious? (Huge point! Learn to detect sarcasm or Twitter will hate you!)
- Does the tweet refer to something the twitterer wrote before?
Please be aware: 95% of all communication via Twitter is exceedingly trivial. Don't fret over it!