I'll second the vote for Gorilla Glue. It's a bit more expensive than Titebond, but you use a lot less glue. It reacts with moisture to cure, so you run a thin bead on one piece, spread it out with some laminate or popsicle stick, lightly mist the other piece with water, and clamp up. Really simple to clean up overrun, any glue that seeps out when you clamp turns into crispy foam when it dries. I seem to get about 20 mins working time, which is long enough to make sure it's right after adding enough clamps to hold it there.
Aside from being more expensive, it also surface cures in the bottle, giving a nice crust on the top of the glue. Either store it upside down, or get small bottles. I've been seeing little 4oz sample bottles at the hardware shops that are about right for my glacial project pace.
A note about wearing gloves: it has a long working time, so it's unlikely that you'll glue your fingers together. However, it will darkly stain your skin (wears off in a few days, don't ask me how I know this).
After you've got it all glued up, planed down, and looking just right, the local kitchen store will have bottles of food-grade mineral oil. Perfect for coating wooden utensils and cutting boards, helps to keep them looking nice and makes cleaning easier.
-jon-