Four ways:
1) Write your own code. This means getting to know the winsock library very well and is in general a LOT of work. But it is the only way you really "create your own browser".
2) Embed IE in your app. A lot of COM, but far less work. MFC does the most work for you if you want to use it.
3) Embed Mozilla. More work than embedding IE, but I like Mozilla better . Embedding Mozilla is described at mozilla.org
4) Create your own derivate of Mozilla. There are several projects like this, e.g. Phoenix or Chimera. Much more work than embedding, but much less than writing from scratch.

I can't think of any other ways.