One example is to write down any excessively negative thoughts and analyze all of the logic errors contained within- such as magnification, all-or-nothing-thinking etc.
The second example is to progress through a hierarchy of situations that may promote social anxiety. For example, as an early, simple exercise, you would start with being around people in a public place like the mall, and just concentrate on enjoying yourself. Then you would do things like speaking up more in a class, voicing your opinion more when you are in a group of people etc.
I disagree with the current scientific thinking about what AS entails. Current research focuses on how aspies fail to discern subtle social cues like facial expressions etc. I instead focus on how we aspies differ in our way of thinking and motivation from NT. AS people are more driven and goal oriented and inner-directed in their thinking. That is why they interrupt a lot, and bore people, since they fail to notice that people are not listening to them. A lot of NT people make a lot of awkward moves in relating to people, so aspies don't have a monopoly on nerdiness. Rather aspie people have different motivations than NT people.
Compared to aspies, a lot of the way NT people relate to each other involves a lot of social rituals to just reassure each other, and provide a sense of bonding and belonging. There is a lot of coversation which is just passing the time, and a lot of just hanging out with no clear goal. There is a lot of ambiguity. Also, there is often a lot of casual touching of the backslapping variety, something many aspies detest.I have my foot in both worlds, so I see both sides.