The best guide to the Internet is the Internet itself, but that's a bit too recursive for comfort and does not help much if you're an Internet novice. The second-best introduction could well be the Virgin Guide to the Internet, which covers all the basics in one pocket-sized volume.
The book kicks off with a short historic overview which explains what the Internet is and where it came from, followed by some 100 pages on basic techniques, from searching the Web to chatting on newsgroups. The rest of its 300 pages are taken up with a categorised directory of useful Web sites and other resources. Experienced Net users will probably benefit more from this Web index than from the instructions.
While it's a bit biased towards the UK, the Virgin Guide is still very useful elsewhere, particularly in its practical, goal-oriented approach. In the section about choosing an ISP, for example, the author lists a number of basic statements, such as "I'm stingy" and "I want to check my e-mail as I travel around the world", then gives simple recommendations as to the type of provider that would best suit the needs of the person making each statement. Since there are hundreds of ISPs, this technique makes choosing one much easier.
The only way to become truly adept at using the Internet is to practise, practise, practise. But with the help of this book, at least you won't look too much like a newbie while you do that.