I am actually a kid, haha. I've never written an actual compiler before or designed a language, but I have finished The Red Dragon Book, so I suppose I have somewhat of an idea (I hope).
It would depend firstly on the grammar. If it's LR or LALR I suppose tools like Bison/Flex would work well. If it's more LL, I'd use Spirit, which is a component of Boost. It allows you to write the language's grammar in C++ in an EBNF-like syntax, so no muddling around with code generators; the C++ compiler compiles the grammar for you. If any of these fail, I'd write an EBNF grammar on paper, and then proceed to do some heavy recursive descent parsing, which seems to work; if C++ can be parsed pretty well using RDP (as GCC does it), then I suppose with enough unit tests and patience you could write entire compilers using RDP.
Once I have a parser running and some sort of intermediate representation, it then depends on how it runs. If it's some bytecode or native code compiler, I'll use LLVM or libJIT to process it. LLVM is more suited for general compilation, but I like the libJIT API and documentation better. Alternatively, if I'm really lazy, I'll generate C code and let GCC do the actual compilation. Another alternative, is to target an existing VM, like Parrot or the JVM or the CLR. Parrot is the VM being designed for Perl. If it's just an interpreter, I'll walk the syntax tree.
A radical alternative is to use Prolog, which has syntax features which remarkably simulate EBNF. I have no experience with it though, and if I am not wrong (which I am almost certainly going to be), Prolog would be quite slow if used to parse heavy duty programming languages with a lot of syntactical constructs and quirks (read: C++ and Perl).
All this I'll do in C++, if only because I am more used to writing in it than C. I'd stay away from Java/Python or anything of that sort for the actual production code (writing compilers in C/C++ help to make it portable), but I could see myself using them as a prototyping language, especially Python, which I am partial towards. Of course, I've never actually done any of this before, so I'm not one to say.