It looks like a center tapped transformer. check the voltages with an AC voltrmeter, if you have 24 V between some of the black wires, it is a center tapped transformer. If so use a two diode rectifier as shown here:
https://en.wikipedia.org/wiki/Rectifier#Full-wave_rectification
Scroll to the center-tap image with two diodes.
If you need 500mA DC supply, a 500mA transformer is too small, you should have > 900mA
To fill the dips that go to zero, use a 3300uF (or larger) capacitor after the rectifier (observe polarity). Measure the output with a voltmeter with a 500 mA resistive load (that is large resistor of 28 Ohms). Do this for short term only, as you are overloading the transformer.
When using 3300uF capacitor, the ripple will be 1Vpp with 500mA load. A LM7812 needs about 14 V input voltage (at 1A output). So the reading on your voltmeter should be around at 14.5V. If you have significantly less voltage, you can't use the LM7812 and in that case you need to find a "low drop out" regulator (or complete other solution).
When you have about 14.5V, you can use the LM7812. Make sure to read the application info to avoid parasitic oscillation (and EMC issues with the pulsed RF signal from the GSM modem).
Your modem will very likely use max 500mA peak current during the on cycle of the RF PA only (due to the time slots in GSM). The average current during transmit will be very likely less. So when the rectified voltage at 500 mA is (for example) 13.5V, the regulator may do the job as the average load of say 100mA will result in more rectified output voltage. The current peaks are drawn from the 2200uF capacitor.
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If you use your new 1A transformer, this should be fine. I would use somewhat larger rectifier then 1N400X as this results in less voltage drop across the diode (and less generated heat in the rectifiers).
2200uF instead of 3300uF is fine, as the output voltage with 500mA load is higher, so you can accept more ripple. If you have an oscilloscope, you can check the rectified wave form when drawing (for example) 500mA.