You may find that distilled water tastes different from the water you usually drink. Distilled water is largely tasteless as it is free from chemicals and minerals (source). If you have been drinking water containing impurities or minerals, you may notice the lack of taste more than anything else.
If you are struggling to get used to the taste, you may find it easier to drink your distilled water cold. Refrigerate it after the distillation process in an airtight container. You may also find that adding a slice of lemon helps you adapt to the new taste.