I don’t normally use Illustrator, but when I do, I like to keep everything centered on the artboard, or the huge green square in the center of the screen. It’s actually quite easy.
If you have objects that need to be aligned, select them and then
Object > Group. This puts them in a group and they become safe from the alignment themselves; their center point is what is centered. Then use the selection tool or more informally, the black mouse. Then in the middle of the attributes bar, there is a black-square that allows you to specify alignment – either to the artboard or to the crop area. Choose the former. For a center alignment, use Horizontal and Vertical center align and that’s it. You might also want to ungroup your previously grouped objects, but that’s up to you.