Skills are important for role playing in D&D 4E.
Ideally, if a player wants his or her character to do
something the DM should be able to map it to a skill.
Players shouldn't feel bound by their skill list to try
There are a few things I do to promote role playing using skills:
1) Explicit checks
Sometimes people want to solve a problem simply by doing a skill check.
For example "I roll for Diplomacy" or "I roll for Bluff"
Then I ask them what exactly they say or use the skill for.
2) Say yes
When players have an idea, try to help them translate it into a skill change.
Players should focus on the things their characters would do,
the DM can help with finding skills.
3) "What do you want to accomplish?"
When the players are unsure what to do, you can ask them
"What do you want to accomplish?". Or what does your character
wants to accomplish?
That way, the DM helps the players with finding the correct skills.
The Serious Skills series goes over every skill and tries to find
as many uses as possible for each skill.
4) DM rolls, not the players
If the DM rolls the skill check, players don't know how good it was.
This discourages meta-gaming, for example:
When the players roll a 20 on Insight while talking with a
suspicious figure, then the players will know more than the characters.
This may lead the players to to trust this figure while characters
would not have a reason.
I let skill challenges flow naturally, so I throw the rules pretty much away.
I prepare the situation in enough detail to handle most player input.
The PCs get into a situation where combat usually won't make much sense,
meaning I will not announce it is a skill challenge.
I might have an idea of skills that can be used, and I might write them down.
But these aren't set in stone, I try to say yes to possible solutions
and help the players map their character actions on skills.
Failing the skill challenge sends the story in a different direction, never a dead-end.
Story-wise the situation may get worse for the PCs.