Introducing a new game into a group something that I've done a fair amount over the years, after all I do like to buy games so unless I'm happy for them to sit on the shelves unplayed I am going to introduce them eventually. Is there a set way to go about it? Not really. I mean there are things you should do and shouldn't do but there isn't one way of doing this so what I'm saying here is some guidance rather than "how to do it".
New Game - Established Group
Should do - Bringing your latest purchase along to your gaming sessions still in the shrink wrap is something I've done many times. Mainly because I tend to not have/make the time to take a good look at the game before I take to my gaming group. The benefit here is that your fellow gamers will be just as interested in playing the new shiny game as much as you are and you might be lucky enough to have someone who will do the rules bit for you!
Shouldn't do - Well there's not much that can go wrong here after all the group are all gamers and all have a certain knowledge of the games that constitute the hobby. What you have to be wary of though is only playing new games as that can dilute the enjoyed of the hobby not to mention dilute the value aspect of your hobby. You also have to be aware of the types of games that your group like. Turning up with the latest expansion for a game that you know those gamers didn't like the core set of is probably a non-starter...
New Game - New Group
Should do - The presumption here is that whilst the group is made up of non-gamers or perhaps fledgling gamers they all have enough of an understanding of the hobby. Best to go with something that you know reasonably well (so not still in the shrink wrap!) and that isn't too heavy on the strategy or the luck side of things. If it's a licensed game then make sure that the group are at the very least familiar with the setting and don't dislike it!
Shouldn't do - Don't bring anything that will take 3 hours to play in a 3 hour slot. It may look awesome and indeed it may be awesome but if this is a new game for a new group then you will need to go over the rules a few times to clarify things which will eat into that time. Plus it's best to have a game that gives you the chance to play it more than once if the players enjoy the first run.