If you are travelling from within Europe, there are some very reasonable flights with companies like Wizzair and Jet2 etc to Budapest.
There is a train service from Budapest to Arad and from Arad there is a bus to Taut. For more information about bus links then contact us, since these vary from time of year to time of year.
It looks like Ryan Air are about to begin flying from some locations to Arad via Milan. This is something that is worth checking out.
Below is a map showing how to get from the City of Arad to Taut.