Hi Stu,
I'm a beginner in this field, so definitely take the advice of the more experienced here above mine.
The standard first step is a Paton Hawksley Star Analyser SA100 -
http://www.patonhawksley.co.uk/staranalyser.html. Even if you end up moving up to more advanced equipment, you will still probably use an SA100 once in a while, so this is a no brainer. The SA100 is very basic, it is a diffraction grating mounted in a standard 1.25 inch filter holder. The grating contains many fine parallel lines (100 per mm) which cause any light shone through it to diffract into a rainbow. Currently costs 92.70 GBP.
The SA100 is designed to work with a camera, as opposed to be used visually. It will work with a DSLR, but you will get the best results with a mono CCD. It is somewhat counter-intuitive, but you don't need a colour camera to take spectra. I use a mono QHY5 guide camera, others use proper mono CCDs.
The SA100 is most commonly used in a telescope, basically threaded into the camera nose piece. However you can also use it to great effect with a DSLR lens. See Rob_K's excellent results on the nova thread.
Using an SA100 will get you acquainted with processing spectra. The standard free tools are VSpec (
http://www.astrosurf.com/vdesnoux/) and ISIS (
http://www.astrosurf.com/buil/isis/isis_en.htm). There is also RSpec (
http://www.rspec-astro.com/) which is not free.
Ken's book 'Astronomical Spectroscopy for Amateurs' is an excellent introduction to how to take and process spectra. There is a great section on processing an SA100 spectrum with VSpec.
A great free PDF book is Richard Walker's Spectroscopic Atlas (
http://www.ursusmajor.ch/astrospektr...-walkers-page/). This shows examples of various spectral types and explains some of the features you will see when you start taking your own.
To understand some of the theory behind spectroscopy, I found 'Spectroscopy - The key to the stars' by Keith Robinson (
http://www.springer.com/astronomy/as...-0-387-36786-6) a fantastic read. Most books on quantum theories touch on matters related to spectroscopy too, the two are tightly linked.
I think it's kind of like marmite, some amateurs just don't see the appeal. Others, once they've had a taste, just can't get enough of it!