After speaking with Sir Radzig in Pirkstein it will probably be late in the day. The best thing to do before you begin your training with Captain Bernard is to get some sleep in Rattay Mill. You can also sleep in one of the beds in the refugee camp at the lower gate if you wish.
You will find Captain Bernard at the combat arena outside the Upper Gate of Rattay. Note that he will only be there after 8am, so you may have to wait an hour or two depending on how much you slept.
Once you are done going through the motions of combat with Captain Bernard, follow him to the archery range. After taking a few practice shots, Henry will find himself in a confrontation with Sir Hans Capon. An archery content between the two ensues. Regardless of the outcome a sword fight will follow that. At the end of the sword fight you will be instructed to report to the Bailiff, who can be found in lower Rattay. Remember to wash yourself in a trough on the way.
The Bailiff can be found by walking up the stairs to the right of the Tailor shop. Once inside, go through the hallway and into the main room where you will find the Bailiff working at his desk.
As you speak to the Bailiff be sure to ask him about any other work that might be available in and around Rattay. You can come back to him at any time to see if he has any new quests.