Aligning multi-color woodblock print? I know how the registration of wood blocks works in the Japanese-style wood block printing method (put registration marks on the block to align the paper: see this YouTube channel). Since the woodblock is wet with paste and pigments, the paper adheres to the block and the print can be rubbed off by hand with a barren. 

How does registration work with European-style wood block printing, where a printing press is used instead of rubbing by hand with a barren? I imagine that, if you don't fix the paper on the block in some way, the paper might shift while you slide the block (and paper) through the press.
My bachelor's degree was in Fine Arts, with a focus on wood block printing. 

The technique I was taught involved marking the center line on the back of the leading edge of the paper. (The end that will feed into the press first.) On the press, lay out a registration paper that clearly marks the location of the block, a corresponding center line, and one or both leading corners. The block is inked and laid on the slab. Then, align the center lines and corner marks, with the other end held high. Slowly "roll" the paper flat onto the block while keeping the leading edge aligned. This minimizes inappropriate contact and ensures a flat lay on the block. The ink will loosely hold the paper in place.

Once the paper is laid, heavy felt blankets are usually laid over the entire thing. There is the chance for paper movement here, so again - a careful "rolling" action from the leading edge back is best. Make sure the weight of the blankets is centered over the block as you do this. These blankets then keep the paper in place while printing, as well as enhancing print quality and embossing.

Ensuring that your press is set to the appropriate height is very important too. Too much pressure will cause damage to the paper, or movement of the block and/or the paper. Once printed, the blankets and then paper are removed in a similar but opposite method.