Welcome!
Firstly, a photo or two of what you're looking at would be very helpful.
The transformer has three wires running out of the transformer towards the circuit board. I've tried measuring the voltage but because it's AC I cannot get an accurate reading. If I measure the voltage after the diode i'm getting around 5.42 volts.
You should be able to get a proper reading using a meter that is set to the correct range to measure AC voltages. What kind of meter are you using? Perhaps a photo of that, as well.
Also, there is usually more that one diode, often what is called a bridge rectifier (which is actually four diodes in one package) with four leads.
My question is if I disconnect the three wires: Two of them are the AC and one is ground.
Typically when there are three wires on a secondary winding, it is a centre-tapped winding. This means that there is a winding with two "halves", with the third wire being connected to the point between the two halves, where they join. This is a very useful feature for many applications for various reasons and purposes.
There should not usually be an actual ground wire, though, since once you are om the
secondary side of a transformer, you arbitrarily call some point of your circuit "ground" potential, even though it may not truly be earthed. Photo, please.

And if someone can give me some safety advice that would be great!
Firstly, since you are a beginner and don't want to be anywhere near the mains power yet, if you must experiment with a mains connected device, even just a transformer, be absolutely sure that all connections that are at mains potential are fully insulated! Starting by using battery powered circuits or a self-contained wall-wart type power supply may be more appropriate, however, as long as things are truly insulated completely, the potential danger can be made to be minimal.
Again, if you provide some photos, we can help to see if this clock is insulated well enough to be in there poking and prodding around when you're just starting out and learning.