[Boromir88]

I think some other smart moves done by Aragorn that haven't been mentioned yet, is actually his humility he shows to Boromir.

Aragorn's claim is brought out in the Council, and although Boromir hasn't yet accepted Aragorn as King he admits that Gondor is in some desperate times and the "sword," would be of some great help. He is yet unsure of Aragorn, however. Aragorn knowing this, plays humility towards Boromir, trying to win Boromir's trust. Knowing that Boromir may very well be the most prestigious man in Gondor. His title is "Captain-General of Gondor's forces." In common day terms that would be like "Commander-in-chief." And supported by Denethor it is not him who leads his men, he sits back in his hall, and leaves the leading up to his sons (at first mostly Boromir, then once he's dead Faramir). Also, Boromir is to be the future Steward of Gondor. Aragorn recognizes if his claim is to fall through he will have to get the approval of the Steward, as well as some of Gondor's most prestigious men.

So what does Aragorn do? He shows humility and actually takes orders from Boromir. On Caradhras Boromir says he and Aragorn will carry the Hobbits, Aragorn possibly in an attempt to buddy up to Boromir, doesn't object, and out of the respect of Boromir's status, listens.