LTS, you're right, it is a "brain thing". It's a skill, which has to be learned. The trouble is, because the mind is such a slippery and poorly-understood thing, it's difficult to explain to someone how to do it. Everyone will have their own method which works for them, but to find it is often a matter of trial and error.

For me, it comes down to repetition, over and over. When a song is new, and has caught my imagination, that's not a problem for me, I enjoy it. I prefer to work on the whole song and go back to fill in the gaps, whereas others may prefer to build it up a line or two at a time until they've memorised it through to the end. Whatever works for you.

Once I've got it, I keep repeating it - in the car, in the shower, as well as more formal practice. This reveals those points where I have particular difficulties - perhaps a similar phrase which keeps getting muddled up, or something which refuses to stick - and I know I have to remember to concentrate at these points. As I usually accompany myself, I will also be working on the instrumental arrangement, which evolves over time so I have to decide when I'm happy with that and to start consolidating the whole thing in my mind.

It may take two or three weeks, perhaps more, of daily practice before I'm ready to perform it in public. I usually try to road-test it in a fairly informal setting where it will matter less if I make a mistake. This is also an opportunity to identify points where nerves (which all performers, however experienced, get from time to time) get in the way - perhaps the arrangement is too difficult and needs to be simplified. Once the bugs are ironed out the song is ready to be performed.

It's a lengthy process, and takes time and effort, but it means I have explored the song in far more detail than would be the case if I were to sing it from a book, no matter how many times I did so. Sometimes I think I only start to do a song justice after I have become bored with it, left it for a while, and then come back to it. Songs need time to mature - again, unlikely to happen if you rely on a book every time.