Hi Dorothy! The instructions to find this information out do vary some based on the model of Kindle, but will be similar to this:
1. Press the Home button, then press the Menu button.
2. Navigate to Settings by moving the 5-way controller down, then press the 5-way controller to select.
3. Select view next to Wi-Fi Settings to display a list of detected Wi-Fi networks. The network you are connected to will show in this list.
I hope that helps! If you need additional assistance, please let me know which model Kindle you have and I will provide better directions to you.