So in order to add to some already great answers, here are my 2 little pence.
It was already written here, but it can't be stressed enough. The basic idea is that through questions you do 2 very different things that help the character to form. The first one is that you give a lead to the past or present of the character. If I ask a character "How do you feel" it means among other things that this character has feelings while also that they influence what she does right now. If I ask if she has been here once, well it gives a lead to an event in the past where she did spend some time in here.
The second thing, though, is that it forces, albeit subtly, the player to enter into the mindset of the character. It helps her to see through her character's eyes, to feel through her feels and so on. This helps her to create a bond, a connection to her character. From there, advancing to roleplaying is a lot easier.
Another small benefit is that most conversations between people start and revolve around questions and their answers (which lead to more questions and the cycle goes on). Thus, it means that you let her take part in a conversation as her character. No need to explain how it helps to explore the character, I hope.
If you'll let me borrow a term from the improvisation world, suggestion is anything that you do or say that starts the imagination of other people. The idea here is that you should try to influence the other players' imaginations in order to make them start rolling. In can be in the shape of "remember that time when…" in the shape of "wow, what is this sword in your bag…" or anywhere in between. Something that makes the player think a little bit about what it means, something that gives the character a lead to think from, a spark of creativity that she can build upon.
Lead from example
Make yourself an example for how should one play. Play it personal, try to explore your character through the story, try to find within the character those extra levels and use them to show the other players what they're missing right now and what they can achieve. Extra credit if you can make it seem relatively simple. Not all players like to give everything they have in terms of time and resources to a character in a game.
Ask them for help with your character
Some players are just afraid to ask for help, so by showing them that you fear not of such a thing you give them a reason to ask for it themselves, not to mention using this help. It is another kind of example, but with a benefit: Many a time, after helping someone else to explore his character one's subconscious starts to look for similar things to do with her character.
Give them time
You said it yourself that some of them do need some time to flesh their characters. By forcing them to do it more quickly that they need or want you can damage their exploration of the character. Wait for the right moment, when they'll show signs of starting those engines, and only then start to help them. More than that, you should always let them explore their characters in their own pace. You can help, sure, but don't rush them too much.
And an end
I'm all hope that any of these ideas will help you. Always remember, though, that these are just some ideas that I used in the past and that they may not be the perfect and ultimate solution to your problem. I do hope that they worth a shot.