Such shenanigans aren't exactly uncommon between nation-states here on Earth. Why would space in the 24th century be any different? You'll recall that Kirk and Spock's successful theft of an improved Romulan cloaking device in TOS Season 3 episode The Enterprise Incident didn't provoke a war between the Federation and the Romulan Star Empire.
It seems likely that both sides simply chalked the incident up to a failed espionage attempt by the Romulans, shrugged their shoulders and continued business as usual. The Federation certainly needed to avoid an open conflict with the Romulans at a time when the Dominion and Cardassians were on the move, with potential problems with the Klingons as well. Sometimes in geopolitics you need to simply suck it up when your neighbours pull an outrageous stunt, because making an issue of it would cause more damage than simply ignoring the issue.
Look at the fallout in Europe from the recent revelations of American spying released by Edward Snowden for a real life example. Several European nations were angry and demanded an explanation, but they haven't left NATO, they haven't declared war and they haven't broken relations with the US. The attempted theft of Prometheus by the Romulans would seem to fall into a similar category.
As for how the Romulans stole the ship, that I couldn't tell you. It's been far too long since I've seen that episode. I'm not sure we're ever actually told how.