So I'm really new to the whole database thing.

Now I have a website running here. http://fcsit-trackandtrace.comuv.com/
You don't need to register, as the member's area is empty right now.

Now what I want to do is, when someone logs in, he will get this sort of service where he can get an information out of a database.
Eg. He puts in a code in this box and then submit, then the website will check within a database and it will return "Your parcel has arrived" etc.

Also, I would like the members to be able to put in more than one code at a time having a semicolon to differ the codes, like a forum tag as an example.
As like xxxxx; xxxxx; xxxxx

Any help on that?

We are not going to teach you everything you need to know about databases. I suggest you do a little googling. You can start with W3 SQL Tutorial.