Images, Slides, Videos and Albums
Use the Insert menu for images. Click 'Images' to select from your Drive/Photos. Use Upload to select from your computer. You can upload only images. You can also double-click to get the "Compass Menu".
After inserting an image, click the 3-dot icon and you can select to add alt text. Double click the image to get the zoom/crop option.
You can drag the dots to resize the image. Hold the shift key to prevent cropping. Click the image to see the crop, uncrop, link and more options.
Picasa embeds have been deprecated so it is recommended that we move to alternatives for slideshows.
Here are some alternative methods.
Google Slide - - Under Google Embeds >>Slides
The presentation must be shared. I have this one set to Public on the Web. You can select to auto start, loop playback and change the delay time. I think these options are new. Click the slide then click the settings icon (gear).
Note that on a mobile device the presentation will not auto-start. The viewer must click on the presentation to bring it up and then click the play icon.
Also see photo-gallery-from-drive
Unfortunately YouTube Photo slideshows have been discontinued.
To insert an individual image from Google Drive click 'From Drive' in the insert menu. Find your image and click it. Then click 'Insert' at the bottom.
This image is in a folder with sharing set to "Anyone with the link can view".
I got the shared URL of the image and added that link to the image. so viewers can click the image to see it full-sized
Google Photos Animation
This involves using the animation feature in Google Photos. The procedure is explained by Peggy K, a top contributor in the Blogger forum. You can find her post about this in Google+. She explains about using it in Blogger but as you can see it also works in Google Sites. You should view her detailed instructions but here is my condensed version:
In Google Photos click the + icon at the top (Now it is the CREATE link. On mobile click the 3-dot icon)
Click to select each image you want to include
Click the Create button
Click the more actions icon (3 dots) and add the animation to a shared album
Right-click the animation and copy the image URL
In your site click Insert, select Image and then Web address (URL)
Insert the URL you copied in step 6
To make a slower animation you can use an editor like LunaPic. You can upload your fast GIF, change the speed, save the image and upload it to Google Photos, get its URL and insert it into your page. (Don't forget to move it into a shared album)
Example of a cropped, zoomed in, image.
Before cropping it I captured the URL of the image. Then after cropping it I added a link to the full-sized image. The result is that the viewer can click the image to see the big image. To make a link, click the image and select the link icon (looks like a chain link).
New Sites does not automatically make a link to the original image, thus requiring the above method to be used. You can send feedback to Google to request this feature.
See the video here for cropping and zooming instructions
Video hosted on Vimeo. Note that full-screen works (it didn't work on classic sites).
Get the Share URL for the video and use the Embed URL function in the insert menu.
A YouTube Video
Get the share URL and use the Embed URL function or select YouTube in the Google Embeds section or you can embed videos from Google Drive, just choose the From Drive option on the Insert panel.
Sharing options in Google Photos for the above album.
To embed an album get "Link to share", go to that link and copy the resultant link from the address bar and use it in the Embed URL" edit function.
It will look like "https://photos.google.com/share/AF1QipMgvQVQTf_UG5QOZ5LpQ2uAEJGTswy_SgFoVmR-mp0Nw3ITwXlnkqxPwRkvxVLbFQ?key=eVRkQ2VzMVlGVWlqQS11SzFIeFA1b2FBZzlNX2Fn".
<--Animated GIFs inserted from Drive work and repeat.
Video hosted in Google Drive
Upload the video to your Drive and share it publicly.
Insert the video by using From Drive in the Google Drive section of the INSERT menu.
You will not be able to view the video if the network you are on does not allow streaming.
This image added as a background of a text box. Note that such images can't be resized. To be able to resize the image you need it insert it directly, not in a text box.