It would really vary depending on the child. But kids that are sensory seeking in a certain area will basically do lots of things to get input in that area. They aren't getting the input someone without sensory issues in that area is getting. So a child who is hypersensitive to touch might find a haircut painful while a child who is hyponsensitive might bite himself. The hyposensitive kiddo is a seeker of input. As acannon explained you can be a seeker and avoider as well.
But my child was (among other areas) a proprioceptive sensory seeker. That means he seeks input about his body in space. He crawled with his head down on the ground, he constantly wanted tight hugs, he was a head banger, he would jam himself into any tight space he could find, he loved swaddling as in infant, he would hug us really tight and then bite--the biting was to get more input in his jaw, was constantly crashing into people, loves wrestling, stuff like that. Sometimes stuff looks weird with sensory seeking kids...I mean my son would ask you to hurt him! Someone might wonder about that....but he is simply trying to communicate that he needs proprioceptive input. So I offer a good squeeze. He often asks someone for a more "ouchy hug" when they hug him. He means of course he wants a tighter hug.
I mentioned all that because proprioceptive seekers are pretty common it seems and its a hard one to understand and when I look at lists a lot of what my son does isn't on them!http://www.sensory-processing-disord...checklist.html
Here is a link with lists of sensory processing signs. The seeking stuff would be the hypo