Colonel Steven Shay is Carly and Spencer's father. He is a Colonel in the U.S. Air Force, and currently on a tour of duty in a United States submarine. In iWon't Cancel The Show, he was docked somewhere near Anchorage, Alaska. It was implied in the same episode that he is involved in some kind of classified work when Spencer tells Carly that she "probably shouldn't give away their father's current position." But it's also possible that Spencer may have joking.
Dan Schneider, the producer of iCarly, cleared up the confusion about if he was in the Navy, or in the Air Force: he was in the Air Force on a Navy Submarine—this makes sense, as the U.S. Navy doesn't technically have Colonels—the equivalent rank in the Navy would be a Captain.
Although Colonel Shay obviously loves both of his children very much, he's shown to get along much better with his daughter and has kind of an attitude towards his son—such as when Spencer was talking to his dad over the phone about Oystamato and Colonel Shay said he didn't care or when Colonel Shay got mad when Spencer finally revealed that he dropped out of law school (to the point that he almost strangled his son out of anger).
He calls Spencer and Carly in iStill Psycho to make sure they and their friends are okay after being kidnapped by Nora Dershlit (apparently, the events of the episode ended up on the news). Spencer assured him that he, Carly and their friends were just fine.
The plot in iMeet The First Lady revolves around Sam and Freddie trying to help Carly stay in touch with her father on his birthday because he's not able to make it home as planned. He's almost seen in that episode as his face is partially obstructed by static.
He appears in the series finale, iGoodbye, to take Carly to a special father/daughter dance. It was during an iCarly webcast held in the episode that he finally learns that Spencer dropped out of law school. Although obviously angry with Spencer at first, Colonel Shay seems to get over it by the end of the episode, and when Spencer points out that he would've been a terrible lawyer, Colonel Shay seems to acknowledge this and accepts Spencer's passion for art. Spencer later asks him to send more money.
The actor portraying Colonel Shay on iGoodbye is named David Chisum (on his blog Dan Schneider spelled his name incorrectly as "David Chism").