I think I can confidently say this has happened to every single one of us. And if not, then it will. At some point or another you will find yourself in a situation where you have to talk to the most socially retarded person on the planet. And it won't be easy.
From my experience, these conversations always progress through at least four stages. There is a fifth, optional, stage that you must pull out if you are absolutely required to speak to this person on a regular basis. Like, if you married them, for example.
If you can, drink your way through the stages, it'll make it that much more entertaining and much less awkward. Though be warned, sometimes drinking to this extreme is seen as 'inappropriate' or 'raging alcoholism'.
For sanity, it's best if the stages are brief, but more often than not, they're not. If you're at a party or a bus-stop, the stages will progress very quickly. If you go to school with or are related to the socially inept dweeb, the stages will drag on until you would prefer to stick shards of glass in your eyes than continue talking with them.
The first stage is introduction. Often times, you don't realize how socially retarded someone is until you make your first attempt at conversation.
You say hello and they look at you; you introduce yourself and they look at you; you ask them what their name is and their friend answers you. If you make the mistake of trying to shake their hand, they'll look at your right hand extended and then back to your face. Their facial expression will not change. If at all possible, leave the situation now. If it's important that you talk with this person, try to progress through the remaining stages quickly just so you can say "I tried".
The second stage is asking questions to try and get them to talk.
Most socially awkward people will answer your questions with one or two words and will not ask you anything in return. This makes the question-answer stage painfully boring (or maybe just painfully painful); you're going to have to get creative if you want to get anything out of them. But it likely won't work. Don't worry, you'll move onto the third stage soon enough.
The third stage is volunteering information; since they won't ask you anything, you begin providing them with the information that they should be asking for, or random facts and trivia.
I like to tell stories; it's far more entertaining (for me) than telling them about what I do for work, or how I know the person we both know. Besides, that will only work for so long; plus I think that if I tell a story about the most basic life experiences, I will show them just how easy it is and they might reciprocate, even just a little bit.
Sometimes it works and sometimes it doesn't. When it does, it's glorious; when it doesn't, I'm sure the dud is left wondering how I yammered on for 15 minutes about buying milk. Eventually, stage three runs it's course. No matter how hard you try, you can't think of anything else to say to this person. Welcome to stage four.
The fourth stage is where you simply ignore them. Stop making eye contact, stop looking in their general direction, basically stop acknowledging their presence entirely.
This is the final stage for people that you don't need to talk to ever again. It's the best stage when dealing with random people at the bar, or on the street, because if you do it right, even you forget that they're there.
However, in most social circumstances you can't stay in this stage for very long; people will start saying that you're rude, or a bitch. These people have been in the fifth stage for so long that they've forgotten what it's like going through the first four stages with this person. Don't worry, it'll happen to you too.
The final stage is acceptance. You come to realize that this person has made it through their entire life being a social tard and nothing you do will ever be able to change that. Sometimes it's easier to just lay down and take it. Luckily, you won't have to take much, because they likely are still unable to have a conversation with you. You better learn to love awkward silences. My coping mechanism is music - I play music in my head in an attempt at convincing myself I'm having a good time. Oh, denial, you've helped me so ... ... ... wait... no, you haven't; I did it all on my own.
Big thanks to EliseArt for providing illustrations.