Thomas Paine aims his pamphlet at any American who can be convinced that independence from the British is the only way for America to move forward. In making this case, Paine shows his own patriotism by arguing that "the cause of America is in a great measure the cause of all mankind." (I.4)
In other words, the ideals of freedom and liberty have an impact on everyone in the world, and by fighting for independence, American could set an example that might inspire other people to fight for their freedom.
In a perfect world, American patriots wouldn't have to fight for their freedom at all. But unfortunately, this isn't a perfect world and the British are being total jerks. The time for talk is over, and for anyone who agrees with Paine, "Arms, as the last resource, decide this contest; the appeal was the choice of the king, and the continent hath accepted the challenge." (3.2)
In other words, it's time for Americans to stand up and fight for their rights.
Paine fans the flames of American patriotism by talking about how other people from all around the world continue to flee to America hoping to find a place of freedom and opportunity: "Hither have they fled, not from the tender embraces of the mother, but from the cruelty of the monster" (3.11). Unfortunately, they arrive only to find out that the British rule over this place with an iron fist just like everywhere else.
The arguments laid out in Common Sense ultimately lead Paine to argue that the world as a whole won't be able to move forward until America shows everyone that it's possible to stand up and claim your freedom. He writes:
[Until] an independence is declared, the Continent will feel itself like a man who continues putting off some unpleasant business from day to day, yet knows it must be done, hates to set about it, wishes it over, and is continually haunted with the thoughts of its necessity. (4.32)
American independence is going to happen sooner or later, so it's up to the true patriots to step up and take charge.