Dd is 17 months, and has been colouring and painting and doing other little art projects (pasting colourful shapes, etc) at nursery ever since ... well, probably about 6 months old. Of course at first we knew that the carers were actually doing more of the painting and colouring than she was, but it was at least giving her the idea of what to do ...
And now, just the other day I sat her down with a colouring pad and crayons, and she coloured quite happily for a good ten minutes or so. It is neat to see how her 'colouring' has progressed - she used to just make little dots on the page (and that was more by accident than design), but now she makes lots of little lines.
Probably not a Picasso, but it still makes mummy really proud, and gives me something to put on my fridge! :-)
(And working with the crayons gives us yet another perfect chance to talk about colours.)
(Oh - not sure if this is a good tip or not, but when I have coloured with her, I have been extremely reluctant to guide her hand at all - It was really tempting at first to take her hand and move it back and forth across the page, but I was determined to let her do it in her own way, in her own time, and it has worked out well.)
And as far as fear of them colouring everything else - well, I reckon she's going to do that some day anyway (I think all kids do at some point) - We just keep the crayons out of reach and then supervise her when she does use them.
We also have her sitting at a proper little table and chair while she does this, and she seems to really like that, too.