You are correct. The transformer will only reduce the voltage (and increase the available current), so you need to add additional circuitry to rectify, smooth and regulate your 12$V_{ac}$12\$V_{AC}\$ transformer output to 5$V_{dc}$5\$V_{DC}\$.
This is the type of circuit you should be looking to build:
- The transformer reduces the voltage from mains to 12$V_{ac}$12\$V_{AC}\$ (rmsRMS).
- The Diode Bridge (known as a bridge rectifier) will convert 12$V_{ac}$12\$V_{AC}\$ to 17$V_{dc}$15\$V_{DC}\$. The voltage is $\sqrt{2}$\$\sqrt{2}\$ times minus two diode voltage drops higher than the input voltage because the rectifier output is the peak AC voltage, not the rmsRMS AC voltage.
- The first capacitor will smooth out the ripples that come from the output of the AC to DC bridge rectifier.
- The 7805LM7805 regulator will maintain a constant voltage as the load varies. For example if you are switching a light bulb on and off, the current will go up and down, and if you didn't have a regulator then the voltage would drop as the bulb is switched on. The regulator keeps it at the 5$V_{dc}$5\$V_{DC}\$ your microcontroller needs.
- The final small capacitor filters out any noise or interference on the regulated side of the circuit.