Unfortunately, apprenticeships are something of a days-gone-by sort of thing. Blacksmiths these days will teach for money, and ussually nothing less. Aside from this, in an apprenticeship the apprentice would not really do anything meaningful until after 7 years of apprenticeship (which would be spent cleaning up the shop, doing repetative forging (like making nails), and assisting). So. If you found someone who would take you as an apprentice, it might not really be something your looking for after all. My suggestion is to do it with a friend who has a similar interest. I have a friend and we help eachother with the forging, do an equal amount, and learn an equal amount. If you don't have any experience in forging, damascus steel is a lofty goal indeed. I might try it this summer, but only after lots more experience with plain old carbon steels (which are a challenge, especially tool steels). So my question is, how far do you want to go with this? Do you want it to be a career? How much do you know already? Do you already have some experience? Have you read any books on the subject?
If you really want to do it, you will. But examine your motives. If it's to make yourself a cool knife, you can buy one for not too much. Also, you may think that these damascus knives are overpriced, but let me tell you, almost NO handforged knife is overpriced. Just having completed one knife from a soft railroad spike, I can tell you there is a lot of skill and work involved in knife-making.