I am litterally talking about a book such as "C for Dummies" and the like.

Is it possible to teach myself some of the more basic ins and outs of programming?  According to the blurb "no experience is required."  Is that the truth.

I guess its primarily out of casual interest.  But who knows maybe one day I could go on to do some sort of game (or other program) development course.

And if its possible, do I start with "C?"

C can be tricky, and requires good eyesight.
C++ is a bit easier.
You might want to try Java, even though it's a stupid language and only an idiot would code anything in it. But it's popular.

Are C++ and C related?

As in, if I learned C++ and then wanted to learn C would I have a nice leg up?

I recommend you learn C++ instead of C. On a basic level C and C++ looks almost the same, but when it comes to more advanced topics such as memory allocation, pointers and Object-Oriented Programming C++ is the way to go.

My computing teacher learned how to code from a book , can't remember the programming langauge though.

Yeah, no experience required for programming. You just need some logic, you don't even have to be good at maths.

C and C++ are related in such a way that C is a subset of C++, meaning that a program written in C should compile also using a C++ compiler. They share the same basic syntax with C++ having a number of additions over C, but most of programming IS basic syntax, so if you learn C++ you definitely learn C as well.

For ease of learning, though, I would recommend Java. The basic syntax is still the same as C, but you don't have to worry about memory management, pointers etc. and you'll learn objective oriented programming. Just make sure you don't get stuck on Java, learn the basics there and then move on to C or C++ (or even objective-C if you'd like to try OS X or iPhone programming). Learning just Java will lead to some poor coding habits, so it's good to move to the C-family to see what is going on under the hood, so to speak.

So, in a nutshell: Java, C++ and objective-C all have the same basic syntax that is based on C.

Do some C++ ,but don't focus to much on it.

Learn Java first.

Java is more job related. Java is a 'Gateway' to 'internet application programming', and it opens up a lot of doors.

If you want to learn Programming and Object-Oriented Programming in particular, then Java will make it easier for you to learn the abstract concepts.
If you want to really code games, then you'll have to dive into C/C++, but those abstract concepts will then be mostly overwhelmed by lower level concepts and issues. Those low level issues _must_ be dealt with in real world, but i don't think they are a good starting point to learn about Programming in general.

Let's put it like this. It's very simplified but it should give you a good idea. Yes, you can learn programming without experience; how else do you think people would learn it ?:P Of course beginning ought to be the hardest part.