NBC Sports Network has the rights to Formula 1 in the US. Most cable/satellite providers carry the channel nowadays. A few races every year, usually the US Grand Prix, the Monaco Grand Prix, and sometimes the Canadian Grand Prix or others are shown on NBC proper. Some other races (and definitely quite a few qualifying sessions) will end up being shown on the USA channel, which is owned by NBC. This is due to conflicts with other sporting events shown on NBC Sports.
NBC makes sure that all of the GPs and qualifying sessions end up broadcast live on TV, and some practice sessions (especially those in the middle of the night) will be broadcast as well. On top that they usually have pretty good pre-race and post-race coverage, and the commentary team always do a great job. The only negative to the broadcast is how often they cut to commercial, although they now do a lot more side-by-side with the screen split between an ad and the F1. If you're really interested you might be able to catch a few F1 features on NBC Sports, sometimes they'll have features that Will Buxton has made or even F1 documentaries on there.
If you wish to watch online, NBC offers the NBC Sports Live Extra website, but you may or may not have access to that, depending on your television provider. I do not have access to it, but I know you can watch things like Premier League games that they have the rights to but didn't end up broadcasting on air. Whether you can watch what they are actually showing on air or not, I am not sure.
Hopefully that helped, if you have any other questions about watching F1 in the US, or just the US in general, shoot me a message.