I know nothing of programming, but I would love to learn.
Here is what my naive approach would be, which I assume would take about 6-7 months of study.

I would first learn the fundamentals on a bare-bones *nix system like Debian or possibly FreeBSD, using an editor like Vim, and the GCC.
[Fundamentals]
Basic C programming
Basic C data structures

Advanced Unix Programming
Assembly
Computer Architecture and Design

DNS & BIND
TCP & IP
Unix Network Programming

HTML/XML
Apache
MySQL
1 scripting language: PHP, Perl, Ruby, Python, Lua, etc...

Visual Studio (C++)
ASP.net
Ajax

Along the way I would learn about GNU make, CVS, Digital Logic, the Windows Registry, and fully understand a text on Discrete Mathematics.

Some projects along the way might include:
an imageboard
an instant messenger / irc client
a game
a device driver

Professional programmers please feel free to laugh, yet modify and correct.