We're moving into the final PR offensive for New Vegas, with the latest newsworthy entry being an interview with executive producer Tess Treadwell on Big Download. It covers the very basics, so it's particularly handy if you haven't been keeping up.
How was the game's skills and character leveling systems changed compared to Fallout 3?
You'll still level up the same way, but we've balanced a lot of skills, and tried to make them all useful. One skill change some people have noticed is that we've rolled Small Guns and Big Guns into a single "Guns" skill. There's also a new "Survival" skill that affects how useful some items are, and allows you to craft items at campfires. You can also now use Magazines to give yourself a temporary skill boost, so if you fail a skill check somewhere, you won't necessarily have to wait until you've leveled repeatedly to take another crack at it.
In terms of chatting with characters has there been any changes made for Fallout New Vegas?
Dialogue in Fallout: New Vegas is more complex. -- There are a lot more twists and turns you can take in conversations, and there are also a lot of times when certain Skills will open up new dialogue options (for example, you might get an option for your Explosives skill when talking to someone about blowing things up). Even if you won't pass the skill check you'll still see an option, although it'll be obvious using that line will fail. However, failing a skill check line won't bar you from trying again in the future. Faction reputation can also open up new dialogue.
Lastly, I'd say that we have a lot more reactivity from NPCs based on things you've done (or haven't done). Not just as conversation topics, but NPCs will greet you based on your reputation and comment on recent events just as you're walking around.