Personally I’m not so sure why you’d want your voice processed so generically. Sure, she’s got a nice voice, but the audio processing is very dull.
There is such a thing as too much polish.
Anywho, 70% of that is performance. The other 30% is carefully overblown studio work.
First, the mic needs to be very nice, the mic pre-amp needs to be clean, and the recording environment needs to be equally nice. A $200 mic will probably not cut it here, though it might if you have a mic that’s carefully matched to sound good with your voice. In other words, test out as many mics as you can before you buy one. Don’t buy one based only on reviews you find on the internet. Same with Mic pre-amps, shop around. You won’t be able to do much about the recording environment aside from researching about building a better studio, but I’m going to guess your budget won’t allow it.
Second, I didn’t hear many obvious effects except for careful double tracking during the choruses. Basically just sing the chorus twice (or maybe even 3 times) and play the second take quieter than the first, be sure to pan the doubled tracks slightly off the lead vocal.
Third, careful EQ. I didn’t hear any bass frequencies in those vocals, so cut everything below about 350 Hz (maybe even higher). I’m not sure what they did to the high end, it’s impossible to tell.
Fourth, there’s probably an Exciter or an Enhancer subtly applied to the higher frequencies. Audacity doesn’t have any plugins with this effect and I’m not sure how to apply it, I’ve never liked what it does to vocals.
Fifth, there’s almost certainly some form of Auto-Tune applied to make her sing perfectly in key. Which particular plugin is used is hard to say. Antares Auto-Tune is the popular one (I think). However, Audacity also can’t use these kinds of plugins since it can’t support VST plugins (due to legal issues).
Finally, there’s some kind of reverb applied to all of that. But I have no idea how to tell you exactly how to re-create it.
Audacity can be used to make very nice sounds. It is more limited than some other programs (Sound Forge being one of them), but most of the audio quality comes from the person behind the recording. If you want your record to sound like it was recorded by an engineer who makes $100+ dollars an hour, then hire one. It takes a lot of experience to make good records. Plugins can make up for some lack of experience, but plugins alone won’t get you there.