I'm from a similar background, I qualified [barely] in Chemistry too. I also deviated.
There isn't a hard and fast answer to your question, so what I say comes from my experience in the UK so YMMV. The first thing is that, if you want to do this as a career, you might want to consider getting qualified, this will make the transfer much easier. Some parts of the world (I work in the Middle East) won't employ people without a degree in Comp Sci. Personally, I disagree with this, but that is how it is here.
That said you can get a head start by tackling much of the material before you go for you qualification. The classic route is generally:
1. Variables & Data Types
2. Procedures
3. Control Flow statements:
a) Ifs (if x > 2 then go to somewhere else) & switch statements
b) Loops of the various sorts
4. (Seeing as you want VB.net) Object Orientation.
As you are from a numerate discipline, 1->3 should be relatively easy but getting the finer points will take time. You might want to do this along side your web-based stuff. (You might want to check
http://www.w3schools.com/[
^] for excellent web-technology tutorials). Web development brings its own set of problems and you may want to get to grips with the language first. You might also want to consider which technologies you want to learn according to the local job-market, but the above list should give you a
starter. The other thing that is a must is to get to grips with database design and use, doing this properly is not easy.
How you go about this is a bigger question, and it depends largely on you. Some people swear by getting a book and working though it. I personally prefer to set my self a project, and learn as I go, refering to books/online resources as needed. There are a lot of online resources out there that can be used, you just need to Google for them.