How to convert 6V AC to 5V DC
You need two basic blocks, one to convert the AC voltage to DC and another to step down and regulate the resulting DC voltage.

To rectify the AC to a DC you need a full bridge with a smoothing capacitor



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In the output of this you'll get about 6v x 1.414 ~ 8.44v - 1.4v = 7v (the 1.4v drop is caused by the bridge diodes), then you only need to connect a regulator to step this down to 5v.

One option is a linear regulator like LM7805 (note that it needs about 7-7.5v in the input so it may be a bad choice). The schematic in this case looks like the following



If the input voltage is not high enough then you should use low dropout regulator like LM1117 that needs just 6.2v input for 5v output.



Both the mentioned models are linear regulator, what this means is that they vary their series resistance in accordance with the load in order to keep a constant output voltage. Because of that working principle they dissipate the excess power as heat, that power is the product of input/output voltage difference and load current. 

A more efficient option is a switching regulator that has a different principle and operates as a fast switch that changes the duty cycle in order to keep the output voltage constant. 
An example of such a regulator is LM2596. The specific device needs 7v min for 5v output and the circuit looks like



You can use either solution (as long as the input of the regulator is withing specs).