Power Supply

Insufficient specification, I'm afraid. Questions like:
How much ripple? How accurately 9v and over what load range? How much noise? What peak current? Average current? Short circuit proof? Over-load proof? Minimum load? Is the 12v centre-tapped? etc
all have to be answered or at least considered.
The normal solution is to: 1)take the ac and rectify it with power diodes. 2)Smooth the output with electrolytic capacitors. 3) Reduce the resultant dc voltage to that required with a regulator.
The starting point is typically the regulator, if one is needed. So, say you choose an LM138.
"The LM138/LM238/LM338 are adjustable 3-terminal positive voltage regulators capable of supplying in excess of 5A over a 1.2V to 32V output range. They are exceptionally easy to use and require only 2 resistors to set the output voltage. Careful circuit design has resulted in outstanding load and line regulation comparable to many commercial power supplies."
Sound good?
The data sheet and application notes, available online, will give you the circuit diagram needed.
Of course, that could be way more than you need. If ripple, regulation, fault tolerance, etc don't matter - all you may need is a rectifier and a resistor.

The easy way is to use a bridge rectifier (get a big one 25a or so, they are cheap) a capacitor a few hundred MFD at 35v or so. and that gets you a fairly clean 15-16vDC. Then you can use a 3 terminal regulator to whack that down to 9v and scrub the ripple off the top. It is not the most efficient design, wasting 10-15 watts but easy. If you can't find a 5a 3 terminal regulator you can get an adjustible and use a pass transistor to ramp up the amps.

lots of ways to do this. in addition to the other posts you could use a Triac dimmer in the primary side and rectify and filter the secondary.
is the secondary center tapped? a simple FW rectifier and filter cap will get you 8.5 volts... well minus the diode drop
is it really 12 vac or the more common 12.6 vac? in any event if it 12 at 4 amps it will be somewhat higher at 3 amps.

That sounds great Sue but what size resistor and where abouts online do I find the circuit diagram

If you are asking about a power supply of 12v ac to 9 v dc 3 amp consisting of just a bridge rectifier and a series resistor:
A Google search on bridge rectifiers will tell you more than enough about them! Probably almost any one rated at 5 amp or more would do.
The resistor is trickier. A single, fixed value, resistor needs to take into account the regulation of the transformer, voltage drop of the diodes in the full wave rectifier, etc. So, if you know all those things, the value needed can be calculated.
If you don't know all these things: you start with a high value resistor and a true RMS meter across the load and decrease the resistor until you get 9v indicated at the load. I would use a 10 ohm 50W potentiometer and slide it down until I got the right voltage. Then measure the resistor and replace it with a fixed one of the same value. You may need a combination of resistors to get the right value - each of which needs to be physically rated for the power it would have to dissipate.
Bear in mind what the load will get - a supply with an rms value of 9v - as requested. But with an instantaneous voltage that drops to zero and goes way past 9v, many times a second. Any variation in load will see the rms value of the supply change too. Any variation of the 12v ac supply will also affect the voltage at the load.
Not many loads will like or even survive this! Hence, for electronic loads, smoothing/filtering and regulation is almost invariably used in place of the resistor.
Incidently, if you are replying to someone, then including what you are replying to, or a part of it, helps a lot.

For the DC input, connect the 12 Vac output from your transformer to the AC marked pins on a 6 amp bridge rectifier like this one: Put a large electrolytic capacitor across the + and - pins. Something like 33000 uF, rated no lower than 25 volts .
Use an LM7809 and the circuit shown here for the voltage regulator: Mount the transistor and regulator on a good heatsink.
The solution that uses only a resistor to lower the voltage to 9 volts works *only* with a fixed load that always draws exactly 3 amps. The solution with the LM7809 works regardless of how much current the load draws, up to 4 amps.
Ed

im confuseled Sue, wouldn't a DC voltmeter work better?

Aarrrgh! Meant to provide the page # Scroll down to page 20.
Ed

Without a smoothing capacitor, the voltage at this point would be continuously varying.
Now what a dc voltmeter would make of that would depend on what technology it used. If sample and hold - then it would be producing "random" values, depending at what instant on the half-sine wave the sample was taken. Others would show the average value. Others would show the peak value. Using a true RMS meter seemed the safest bet.
I have no idea what the load is - I am trying very hard to think what load would like 3A of 9v full-wave rectified unsmoothed supply. Sticking some filtering on it and adding a regulator IC has become so much the norm.
I have a strong feeling, that I am sure is shared by others here, that the OP doesn't really want a supply consisting of just a full wave rectifier and a resistor. That this won't meet the requirement. However, the OP has repeatedly been told the disadvantages of such a supply and the advantages of other, recommended, solutions - but still asked for details of the rectifier/resistor solution...

my mind automaticly inserted inserted a capacitor even though none was mentioned.
it seems i have fallen into the habit of differentiating between power supply and battery charger :)

The power supply is for an animated kareoke BUCK that plays songs and allows you to talk through it to mproduce movemnets

you need a well filtered / well regulated supply or the audio section will hum.
if you are unfamilier with electronic construction techniques building a supply is going to be more of a hassle then its worth (unless you really want the learning experiance).
the way i might do it: buy a 12 volt (13.8 VDC) regulated supply at the local R shack. buy a half a dozen or so 5 amp diodes. wire these in series each will drop about .6 volts. at 9 volts the buck will sing (in harmony with big mouth billy bass) and life will be good.

It's probably cheaper to just get an old PC supply if that is the way you want to go. They go on Ebay for $5. I have one I will give away for shipping (Dell proprietary ATX) That is cheaper than a radio shack supply and it will be a lot cleaner power. I have had to add additional filtering to RS (ferro) supplies to make them usable.