The only thing that any country can really do to improve its ability to export is to increase its comparative advantage in some way. A country has to identify what advantages it has over other countries and maximize those as much as possible.
In the case of the United States, the most likely comparative advantage is in technology and education. Americans as a group are well-educated and should therefore be able to compete well with other countries in areas needing a great deal of "brain work." In order to maximize this comparative advantage, the best thing for the US would be to improve support for education and for research and development. American firms need to work on producing higher technology using greater brainpower than other countries. The government needs to spend its money promoting education and technological development. This is how the US could increase its ability to export.