OK now "Banner Grabbing" is something you can do if you want to "exploit" one of there services (You need to port scan before doing this). It is the act of getting the program running on the open port that you scanned before. You will be using the command prompt for this.

Example scenario: Just scanned my target and found that port 3306 (Use the port list I included above to find out what each port is for.) I would open up CMD and type the following:
telnet www.yourvictim.com 3306 (or the port of your choice)

You will then get some information back, kinda like a banner (Hence why it is called "Banner Grabbing"). It should give you a name of the program running on that port.

You will then need to exploit it (IF POSSIBLE). Once you have the program name and version (when you did the telnet command, you should have got these). You will need to check that program on a exploit database (See THIS thread for some good exploit databases). If the program is exploitable, USE IT. If you cant find a exploit, try a different port and repeat the steps above.

Before we get started, I want to list some of the different TYPES of exploits:
Perl
PHP
Python
C
C++

They are the most common types of exploits

Lets assume you've done the banner grabbing, and you found the program running that port and you have looked it up on a exploit database (or wrote your own if you're a fucking genius), and you found a exploit. We will say that the exploit we found was for some shitty DoS attack (The program has a weakness to this specific DoS exploit).

How to actually run an "exploit" will not be included in this clusterfuck. You can either find it yourself in another tutorial or consult the exploits documentation.