Your baggage should be checked through to Stuttgart but ask at Singapore to make sure. However you will have to pick it up in FRA and take it to the train. The AIRail Terminal is after immigration. After leaving the plane follow the signs for Exit, then after immigration follow the signs for the long-distance train station which are marked with the letter 'T' (as opposed to the local train station marked 'S'). This will take you up one floor, across the pedestrian bridge and a concourse towards the train station. Half-way down this concourse you will see a sign for the 'AIRail Terminal' (an area with check-in counters) on the left and baggage claims for passengers connecting from plane to train. Train platforms are on the lower level reached by an escalator or elevator.