Having been a mod on other forums before, I can speak from experience that I'm sort of a mirror when it comes to the community. I'm laid back when they are. It's easy to moderate a relaxed forum, and as such I rarely have to show my serious nature when it comes down to actually moderating the place.
I've always thought of being a mod as being a member with a couple extra perks to it. A mod has the direct ability to help bring about positive changes to their community, if they saw the need. They have the ability to keep things from degenerating into total chaos, while still being able to relax and chat with everyone else.
That doesn't leave out the leadership aspects of the job, though. Most people in the community (especially the new ones) look to the Moderators for leadership within the forums they are in charge of. It's only natural, and it goes without saying that a Moderator should set a solid example of what they expect within the community. All in all, if they moderate their own actions first before everyone else's, they set a good, strong precedent for others to follow and abide by, and it'll positively affect their community.
As for dealing with those who break the rules, I've always been lenient as a mod, and I would doubtless carry that trend in the future. I'd edit the post, let them know I've done so and why, and let them carry on with their day. Most violations are minor ones, and they're very rarely repeat offenses -- not to mention they're mostly good people who simply slipped up.
I always keep in mind when moderating the place that I'm dealing with people, not merely potential rule-breakers and spammers. If they are repeat offenders, so be it -- it's on their head, not mine, when I'm eventually forced to issue yellow and red cards to them. Those times are really the few instances when I get really serious with a person, outside of giving them solid RL advice (should they ask for it).
For the most part though, I'm very lenient, and work both with and for the community I help moderate. My main job is to keep it clean for them, and my moderation doesn't really extend past that.