This is my opinion (and conjecture) it will be hard to write a compiler without understanding data structures normally covered in undergraduate (post secondary) Computer Science classes. This doesn't mean you cannot, but you will need to know essential data structures such as linked lists, and trees.
Rather than writing a full or standards compliant C language compiler (at least in the start), I would suggest limiting yourself to a basic subset of the language, such as common operators, integer only support, and basic functions and pointers. One classic example of this was Ron Cain's Small-C, made popular by a series of articles written in Dr. Dobbs Journal in I believe the 1980s. They publish a CD with the James Hendrix's out-of-print book, A Small-C Compiler.
What I would suggest is following Crenshaw's tutorial, but write it for a C-like language compiler, and whatever CPU target (Crenshaw targets the Motorola 68000 CPU) you wish to target. In order to do this, you will need to know basic assembly of which ever target you want to run the compiled programs on. This could include a emulator for a 68000, or MIPS which are arguably nicer assembly instruction sets than the venerable CISC instruction set of the Intel x86 (16/32-bit).
There are many potential books that can be used as starting points for learning compiler / translator theory (and practice). Read the comp.compilers FAQ, and reviews at various online book sellers. Most introductory books are written as textbooks for sophomore to senior level undergraduate Computer Science classes, so they can be slow reading without a CS background. One older book that might be more introductory, but easier to read than "The Dragon Book" is Introduction to Compiler Construction by Thomas Parsons. It is older, so you should be able to find an used copy from your choice of online book sellers at a reasonable price.
So I'd say, try starting with Jack Crenshaw's Let's Build a Compiler tutorial, write your own, following his examples as a guide, and build the basics of a simple compiler. Once you have that working, you can better decide where you wish to take it from that point.
Added:
In regards to the bootstrapping process. Since there are existing C compilers freely available, you do not need to worry about bootstrapping. Write your compiler with separate, existing tools (GCC, Visual C++ Express, Mingw / djgpp, tcc), and you can worry about self-compiling your project at a much later stage. I was surprised by this part of the question until I realized you were brought to the idea of writing your own compiler by reading Ken Thomas' ACM Turing award speech, Reflections on Trusting Trust, which does go into the compiler bootstrapping process. It's a moderated advanced topic, and is also simply a lot of hassle as well. I find even bootstrapping the GCC C compiler under older Unix systems (Digital OSF/1 on the 64-bit Alpha) that included a C compiler a slow and time consuming, error prone process.
The other sort-of question was what a compiler tool like Yacc actually does. Yacc (Yet Another Compiler Compiler or Bison from GNU) is a tool designed to make writing a compiler (or translator) parser easily. Based on the formal grammar for your target language that you input to yacc, it generates a parser, which is one portion of a compiler's overall design. Next is Lex (or flex from GNU) which used to generate a lexical analyzer or scanner, which is often used in combination with the yacc generated parser to form the skeleton of the front-end of a compiler. These tools make writer a front end arguably easier than writing an lexical analyzer and parser yourself. Crenshaw's tutorial does not use these tools, and you don't need to either, many compiler writers don't always use them. Of course Crenshaw admits the tutorial's parser is quite basic.
Crenshaw's tutorial also skips generating an AST (abstract syntax tree), which simplifies but also limits the tutorial compiler. It lacks most if not all optimization, and is very tied to the specific programming language and the particular assembly language emitted by the "back-end" of the compiler. Normally the AST is a middle piece where some optimization can be performed, and serves to de-couple the compiler front-end and back-end in design. For a beginner without a Computer Science background, I'd suggest not worrying about not having an AST for your first compiler (or at least the first version of it). I think keeping it small and simple will help you finish writing a compiler, in its first version, and you can decide from there how you want to proceed then.