I can recommend several, depending on your previous programming in general knowledge and Fortran specific knowledge.
For an absolute beginner (and don't take this in a negative context; it just means you're starting anew, and unlike someone who has a habit of some bad Fortran77 practices, you'll start with a clean mindset) I would definitely go with Chapman's Fortran 95/2003 for Scientists & Engineers. It is an excellent learning book, and although it has some drawbacks they're not important at this stage. It also has a plethora of examples useful in real life. It also emphasises good modern Fortran concepts and ideas (Fortran 90 and newer).
After it, or maybe instead of it, if you're looking for more of a reference book one cannot recommend enough one of the following:
- Metcalf, Reid and Cohen's Fortran 95/2003 Explained (btw, a new edition covering the latest Fortran standard is coming up in a few days) - a classical reference book. Some swear by it instead of Chapman's.
- The Fortran 2003 Handbook: The Complete Syntax, Features and Procedures by several authors; a standard reference book, dealing with the finer aspects of the language. Not important at this stage but just so you know it's there.
Apart from these, which I like to call "the big three", there are numerous tutorials, scriptas and handbooks all over the web (free) and on Amazon. Some links were given in here as well, so I won't repeat those. Also, your compiler is bound to have a good reference manual I don't know about the free g* ones, but all commercial ones do.)
Apart from that, you know you can always ask any question that comes to your mind in here, and on comp.lang.fortran (usenet group; google for a "Usenet client" or "newsclient" and check it out.). Some very(!) knowledgeable people lurk in there.