You can try connecting your camera to your Chromebook via the included USB cable, but without the ability to install custom software to a disc, it likely won't do anything. Instead, you'll need to directly transfer footage from the SD card (which is the approach I take regardless of what OS I'm using). The popular $249 Samsung Chromebook, the Acer C720s, and the high-end Chromebook Pixel all have SD card slots, but the new HP Chromebook 11 does not. See which model you have, as this will determine which approach you need to take.
If your Chromebook has a slot for an SD card, it won't be at all difficult to get photos from your digital camera. All you have to do is take the card out of your camera and slide it into your computer. A window should appear automatically, but if it doesn't, you can extract the Files app from the app drawer and launch it yourself. The SD card should be listed in the sidebar with an obvious name.
The Google+ Photos app is little more than a streamlined interface for accessing the same files you can view at https://plus.google.com/photos/. This means that you will first need to upload your photos to Google+ to take advantage of the app. You can even set your Chromebook to automatically upload photos to Google+ whenever you insert an SD card. To enable this feature, just tap the icon in the upper right corner and open the settings.
Once there, you will see the option to enable automatic import. Check the box next to it.
After uploading your photos, you can use the app to view your images. If you want to organize them, you're probably better off logging into Google+ and managing albums there, as the app is still somewhat limited.
If you don't want to use Google+ to manage your photos, you can use Flickr, Dropbox, or any other service that interests you. Chrome OS might not have an offline photo manager like the ones available for Windows, Mac, and Linux, but if you primarily store your images in a web browser now, you should do the same on your Chromebook.
Image credit:Chromebook Acer C7