Welcome to Android Central! If you have a lot of photos on the phone, it may take quite some time to upload the photos to Google Photos (especially if you have slow upload speeds on your data plan or wi-fi).
Open the Google Photos app, swipe in from the left, tap Device Folders, and make sure every folder that you want to backup has a blue cloud icon associated with it. Then go back to the Google Photos app settings, tap Backup & Sync>Backup Photos, and decide whether you want to back them up over wi-fi only (to save mobile data), or over wi-fi or mobile data.
Although I would strongly advise that you use Google Photos Auto Backup, you can also copy or move the photos to the SD card by using either a file manager app (if the phone doesn't have one preinstalled, try Total Commander), or connecting the phone to your computer via USB and using Windows Explorer to drag and drop the files.