DomRUK - you can use either vowel sound for the flattened pitches - it's a fairly personal thing and some people tend to use a bit of a mixture! For example, people who use the 'a' sound for eg 'ra' will use the 'aw' sound for the flattened la - otherwise it would still sound like 'la'! I just plumped for the 'aw' sound when describing to someone for whom it was new for this very reason - just simpler in this instance.
Lesleyfx - solfa is just one of the tools used in Kodaly teaching. You really DO have to go on a course to start to really understand it and its possibilities, and also how best to learn it - sorry!
It's almost impossible to learn what it's all about totally from a book - but possibly the most comprehensive book for teachers is an American publication entitled 'The Kodaly Method' by Lois Choksy (pub Prentice Hall). It's horrendously expensive but you may find a used copy on Amazon, or a library should be able to get it for you. It has a good introduction to the approach and then detailed rhythmic and melodic learning for 1st-6th grades.
AnotherPianist - eeek, as I said, it's terribly hard to learn solfa by yourself! The way that Kodaly teachers do it is to teach songs which contain a particular melodic element - then the element is given its solfa names. This means that you always have a piece of 'real music' to relate the solfa to, and this also helps if you forget the sound of an interval (eg if you forget what 'soh-me' sounds like, refer back to the beginning motif of 'This Old Man').
With children we follow a particular order of pitch introduction - pentatonic first as it is easier for children to sing in tune without semitones.
However, for yourself I would suggest starting with diatonic major as this is the most familiar to our ears.
Try just singing a diatonic major scale in solfa, with handsigns if possible! (These reinforce the sound/voice connection through kinaesthetic connection).
Then I would suggest making up small sequences, which is a good way to achieve fluency. For example - drm/rmf/mfs/ etc., ascending and descending. Then be a little more ambitious, eg dmr/rfm/msf/ etc.
Try a pattern of 3rds - d-m/r-f/m-s etc., again ascending and descending.
Then triads - dmsmd/rflfr/mstsm etc.
Try singing intervals and naming them, eg d-r, major 2nd/d-m, major 3rd/d-f, perfect 4th and so on.
And yes, of course work out well-known tunes in solfa and practise singing them in solfa until you can do it quite fast and fluently.
I hope this will at least start you off with a few ideas in the absence of a course.
Apologies for the length of this post but there was a lot to answer!!!