What should someone do if he or she feels their heart flutter and race?

See physician. Everybody gets skipped beats, but a run of flutter or racing, especially if it takes your breath away, is reason to get seen for a thyroid check, ekg, rhythm study, and whatever else. Usually these are mild nuisances easily managed, but occasionally they warn of something dangerous. Good luck.
Depends. On severity & duration of symptoms. If fleeting probably just pacs or pvcs....In which case adequate hydration can be quite beneficial. If sustained may be an arrhythmia such as svt & evaluation required.