This first picture is simply to identify the four screws which hold the base on the telephone.  The screws are captive and will not come out altogether.  Once all are sufficiently loose you should be able to lift the bottom away.

Now you will see something like this.  There are 3 screws to loosen now, again they are captive like the last ones.  The screw at the top of the picture is recessed.  The next picture should clarify its position.

This is simply an enlargement of the photo above to clarify which screw to undo.

Once all of the screws are loose lift the assembly but take care as it will only lift about 4 inches as it is tethered to the dial by six wires.  So long as you have it lifted you should be able to turn it clockwise or anticlockwise on the axis of the bell striker.  Rest it gently on the telephone casing and it should look something like below.

At the top of the picture you can see the rollers that the switch hook pins move against and below them I have indicated the spring that makes the switch hooks pop up again.

This is a picture in side the casing which shows the pins attached to the switch hooks from underneath.

 

Just a last picture showing the spring again.  Its conceivable that the whole assembly might be slightly loose and the switch hook pins aren’t locating on the rollers.  You should have been able to tell whether that is the case when you removed the 3 screws after you removed the base.  Otherwise the spring might have broken or just simply moved from it’s normal position so that the spring isn’t having any effect.