In my opinion a very good book is Compiler Construction (pdf warning) by Niklaus Wirth. I've only used the German edition from 1986, but it introduces a small language and how to build a parser and compiler for it. It only teaches you the technique of recursive descent. Recursive Descent is a technique that is currently enjoying a comeback because it is easier with it to produce meaningful error messages than it is when using lex and yacc or other parsing tools. The German book has 115 pages, the English and more recent edition (from 1996) has 130 pages. This seems to me a good starting point in the sense that little previous knowledge is needed and it gets you a feel for implementing some language with Pascal-like syntax. Actually, in the English PDF, it's an Oberon-like syntax, but that's still close enough.

When I first read the book, I skipped over the chapters 1 to 4, as they concern themselves with the theoretical background of the languages that the approach can handle. Looking back over the chapters, I'm not sure whether it was really necessary to skip over them, as they don't seem as dry to me as they did back then. On the other hand, I now have much more experience and also learned the theory of regular languages and context-free languages in university.

Browsing through the PDF, I see that it also mentions bottom-up (yacc-style) parsing and gives a rough outline of it.