Scaffolding via positive and negative feedback
There's no such thing as one true way to "stay in character." In practice every game is determined by the group. However, there are various ways to encourage behaviour you like, and discourage behaviour you don't like. Then debrief after the game to explore what went right and wrong.
Paranoia, surprisingly, offers the best advice I've ever seen in this vein. Encourage actions you want to see happen again and discourage actions you don't want to see. Offer immediate feedback, preferably in a form valuable to the player.
Consider RPG.SE's online game. I wanted to encourage "Rule of cool" and descriptive narrative action sequences. As a consequence, the moment anyone did something "awesome" I'd drop a +2 circumstance modifier in their lap for them to apply to a later check. Humans are animals, but our doggie treats have to be disguised a little.
It's also important to provide negative feedback. After explaining the concept of staying in character: "Act out what your character says at the table, describe what your character does, especially from his viewpoint." and making sure that that concept matches what the rest of the group is doing, penalize the player for dropping out of character.
My favorite penalty is the "In-character lamp." When I'm starting to get quite annoyed with a table for breaking character, I simply declare that every single statement at the table is in character. If it's descriptive, it's what the character does or tries to do. (Note that the in-character lamp is always lit in paranoia.) After an ill-advised comment leads to significant disruption for the player, they tend to learn. They learn because the rest of the group is also providing pressure on the player to avoid the inevitable bad-stuff.
Don't turn the lamp on unless you need to impose negative feedback or the game calls for it. It may be worthwhile having physical props to indicate when the "in-character lamp" is on. Have a huge stuffed die or statue or something and, whenever it's on the table, the in-character lamp is on. Focal objects embedded in simple ritual are a great aide memoir for people. (This idea taken from one of the blog-posts I read, but I can't remember which one.) If the player has legit questions, they can (if nothing else is happening) physically take the ritual object off the table, and ask their questions.
In summary, by explaining the theory before the game and having a debrief after the game, you can offer the player a concrete learning experience. Engaging in positive and negative feedback will profoundly alter player's behavour in respect to the game. Engaging in simple ritual by using a ritual object to focus the game and represent "in-character" time is a good way to unambiguously indicate what mode the players should obey. Go read the GMing section of paranoia for more scaffolding tips. Make sure that the rest of the group is also behaving the same way.