Suppose someone -- a "friend" -- has never seen anything remotely Star Trek-related, with the exception of the Futurama parody episode (which wasn't particularly funny if you haven't seen anything else Star Trek-related). Advice?
And they want to start watching it? Uh, well it's a little tricky. I would suggest Next Generation, for sure, but of course the first season is rather much worse than the rest, and that is where you get to know the characters at all. I actually am not sure if starting in season 2 would really hurt you that much - sure you don't know some things, but on the other hand there are lots of universes that this is the case for, and it's not really a big deal. I guess I would recommend that, and maybe if they have a friend who they are watching with (I presume this is likely the case, otherwise they probably would either already be familiar with it or wouldn't be so interested in picking it up now), then they could spend 3 seconds now and then explaining relevant little bits.
On the plus side, apart from the occasional 2-parter, the show is very episodic, so watching things out-of-order doesn't really hurt you very much. Some other Treks are far less this way (Deep Space Nine got to be, as it progressed, as did Enterprise; Voyager is this way a little bit, but is still fairly episodic. The Original Series is *very* episodic).
It can also depend on the situation, too. If someone really likes old corny sci-fi, they will like the Original Series more. If they are somehow really into the thing (I don't know how they would be without having seen them...), then you could start with TNG season 1. If they like more of the frontiersy space western, Deep Space Nine is better. If they are really going to want fast action, you might start in TNG season 3, or even go for specific episodes.
But it's a lot harder question than with e.g. Star Wars, where they just go watch A New Hope, or Doctor Who, where you start them on "Rose".