Don't know autoCAD, but there's a couple things that might work for you. When moving vertices, hold x to snap to grid, or v to snap to other vertices or c to snap to curves.

If you want to snap objects to each other, try selecting two objects and use the align tool (Modify > Align Tool). Then click the icons that appear around the bounding box that represent the type of alignment you want.

Hope that helps you out a bit.