There are no types! Integer and Complex are just heads that people use in a way that's like a type.

What is your background in programming and software engineering? If you have a lot of background in programming languages, like a grad student in comp sci, I recommend the free book I linked to. However, if you are like most people who program with Mathematica, you don't need to know anything about this stuff and it won't help you. It will instead just be needlessly confusing and frustrating. To learn the basics of programming in Mathematica, read through the Mathemativa virtual book: https://www.youtube.com/watch?v=2wlk9qqPxp4

To answer your question:

Once you've created a head, you use Upvalues and Downvalues to create operations with that Head.

If you're interested in this, you may be interested in reading about how people implement algebras such as Quarternions or Dual Numbers in Mathematica.

Actually you can use the Head-mechanism to build type-like categories very similar to classes in C++. (I did this for various geometrical classes, and for state spaces of (quantum-) mechanical systems.) Once, when one learned Mathematica from Stephen Wolfram's Mathematica book, one found among the Mathematica-supported programming styles also a chapter on the object oriented programming style with instructive examples. I don't know why WolframResearch no longer claims to support object oriented programming. Perhaps there is a general understanding that 'object orientation' implies that there is a mechanism for inheritance. Heads seem not to support inheritance in any direct way. One important way to use user-defined heads is 'function overloading': Assume you have introduced two heads h1, h2. Then you can define

f[x_h1] := ... ; f[x_h2] := ... ;

and when you call f(x) the evaluation will depend on whether x is of form h1[...] or of form h2[...].