Usually programmers use a more sophisticated program called an IDE (Integrated Development Environment) to develop programs. An example is Microsoft Visual C++.
It will syntax highlight your code but also keeps track of your files and projects, is 'intelligent' and keeps track of your variables, classes, function definitions etc., gives you more information about possible errors and much more. All tools which are really useful when programming.
But notepad works fine.
After having coded your program, you will probably have saved it as a bunch of .cpp and .h files. To make an actual program (a .exe) out if it, you need to compile it.
A .exe file is essentially just a long list of simple instructions for the CPU. Simple instruction like add and subtract, but then not written down as the word 'add' itself, but the corresponding binary number which the CPU understands as 'add'.
A compiler is just a program which acts like a translator from semi human-readable code like C++ to the binary equivalent for the computer to read. It takes a .cpp file and spits out a .exe file.
There are quite a lot of different compilers for C++ alone, each with its different quirks. There are simple compilers which must be run from the command line such as the GNU set: http://gcc.gnu.org/.
But there are also compilers are integrated into an IDE. Microsoft Visual C++ which I mentioned earlier has such a compiler. You just press a button on the toolbar, and it will make a .exe from the code you are currently programming.
Some software I would recommend:
http://www.mingw.org/ - A minimalistic command-line compiler for windows, based on the GNU compiler set. It also comes with some other tools.
http://www.microsoft.com/express/Downloads/#2010-Visual-CPP - Microsoft Visual C++ 2010 express edition. A fully integrated IDE for developing C++ applications.
http://www.bloodshed.net/devcpp.html - Another IDE, which utilizes the MinGW compiler. Probably easier to understand and use for the beginning programmer. Also a lot less system-heavy then Visual C++.
http://notepad-plus-plus.org/ - An upgrade from the old notepad to support syntax highlighting, advanced replace and all kinds of plug-ins and tools a programmer might need to write code. Note that this is just a fancy text editor, and does not include a compiler.