1) One point in common, if B=D (circles stick in a common point between AB and CD) OR if A=C and AB > CD (then circles have a common center, but CD circle is inside the AB circle)
2) No points in common, if CD is inside AB, but C nor D doesn't stick with A nor B OR CD is outside AB and D doesn't stick with B (two different circles - one next to another)
3) Two common points, if C is between A and B (the circles make kind of "wedding ring" symbol)
4) More than two common points, if AB=CD (one circle lays exatcly on the second one - infinite common points) OR if A=D and C=B (again "wedding ring" symbol, but with center A on circuit D and center C on circuit B - four common points)
If it looks chaotic, try to draw it - it should help.