To add a photo gallery to your galley page you insert Media as you do in normal posts, but choose Create Gallery(1) from the top left.
Just click and select images you want to add(2), you can drag these around later still.
Click on Create Gallery (3) to add the gallery.
On the next page you’ll see your selected images.
On the top right you can set a few options. The Link to attachment page(1) means they will open in a big slider when clicked, you can set how many colums you want, this is maximum next to each other(2), and if you want them small, large or medium. The type is important here as this will determine the lay-out, you’ll have to view the page to see this working correctly, I recommend the Thumbnail grid.
Under the images you see a field to enter a caption, this will show up as a slider on the bottom of the photo when people hover over it.
You can add more photos with the Add to gallery(3), and don’t forget to save (4).
When done you can still add and edit the gallery. When you view the page in Edit mode and hover over the images a little icon will show up on top, the pencil bring you back to screen 2, the X will remove the gallery.
Check THIS POST for how to add a cool tiled photo gallery