New viewers continue to find Star Trek shows every day. Some start from the very beginning of the series and work their way through while others want to start with a really gripping episode that's usually based upon a fan's recommendation. That can bring them right into the action and get them hooked...or it can confuse them.
Giant Freakin' Robot has suggested that new viewers watch "The Drumhead" as the first episode of Star Trek: The Next Generation. There's no doubt that's an excellent episode, but it references things that happened on other episodes, like when Captain Picard was assimilated by the Borg and became Locutus of Borg or when Worf's father was supposedly in cahoots with the Romulans. While watching "The Drumhead," it's easy to see how a newcomer to the series would be confused. And if someone is confused, it's sometimes easier to switch to another series rather than try to figure out what's going on in an unfamiliar show.
So what's the best way to watch Star Trek: The Next Generation? It's the same way one should watch all of the Star Trek series. From the beginning. Though The Next Generation and The Original Series were more episodic in nature, skipping episodes does the viewer a great disservice as they miss out on some important connections between the characters.
It might be difficult for a sci-fi fan to get into Star Trek at first, especially since they've heard so much about it and are probably wondering what the big deal is all about. And the first season of The Next Generation isn't its best, but without really knowing the characters or what they're all doing in space, a new viewer might end up giving up on the idea of becoming a Trekkie before they've had the opportunity to really see Trek at its best. To start at the beginning is to meet the crew, get a chance to see who they are and why they're aboard the Enterprise, and watch them become a family.