This is something that the Senators - and most of the NHL - are failing miserably at. While out of market fans have the option of Gamecentre Live (though not exactly cheap), in market NHL fans have no legal source for most of the games other than increasingly expensive cable or satellite subscriptions. The only exceptions are the Maple Leafs and the Canucks, who both offer packages for online viewing of the majority of their games for fans in their broadcast regions.
Toronto fans in the Leafs broadcast region can purchase a subscription that gives them access to 51 games online from LeafsTV, Sportsnet and TSN. Vancouver fans in the Canucks broadcast region can purchase all 57 SportsNet games online through the Canucks website.
And what's really scary is that relative to most of the league, Ottawa fans have it good. All of the Canadian teams do, thanks to CBC. All Hockey Night in Canada games are are available free online to anyone in Canada. That at least gets us 19 games this year.
I couldn't find a US team that had so much as a single in-market game legally available online outside of Gamecenter Live or services tied to having a cable or satellite account.