You don't (normally) switch mains with MOSFET. You use a solid-state relay using a triac internally.
simulate this circuit – Schematic created using CircuitLab
Figure 1. Solid state relay.
SSRs come in two flavours - zero-cross and non zero-cross. For your dimming application you need non zero-cross so that you can switch on at any point in the cycle.
Figure 2. Dimming by phase control.
Your controller circuit will need to detect the zero-crossing point and trigger the triac after the required delay.
Choose a triac to match your line voltage and the required current.
You are working with main voltages. Keep these very separate from your low-voltage circuits. Use good wiring practices.