Is there an official way to take my DVD and put it on my iPhone?
There isn't an "official" way but a common and easy method is to rip the DVD with a utility like HandBrake and then drop it in iTunes to sync with your iPhone. The US Supreme Court ruled that
nothing in the agreement prevents you from making copies of DVDs. Nothing requires that a DVD be present during playback.
So yes, it is legal. source
Actually, it's pretty straight forward.
I would recommend the program RipIt by the little app factory if by official you mean a commercially available and supported software to accomplish the task of ripping a commercial DVD into a format that will work with iTunes to play DVD content on iOS. There are free solutions, but I prefer paying for an interface and a manual and most of all, support and someone paid to develop new fixes to the ripping software when new discs come out with different tricks to prevent ripping. (It's a game of cat and mouse between the movie studios and the rippers unfortunately.)
The company is very responsive in supporting its customers and has been around for some time. Well worth the money for the time and aggravation it saves me. Their passport bundle is a great value if you will use more than two of their products.
If you want legal advice whether doing this is wise, do check with a local lawyer.
The best, and also a very legal, way to go would be Handbrake (as styfle says), however many DVDs come now with a digital copy, where you get a code which can be used to download a copy for iTunes (full DRM so only in iTunes), from there you can sync it to your iPhone. This method is probably easier for a non-techie (although Handbrake is pretty simple), but it's a lot more restricting.