In this tutorial I assume you already know how to make a gif (x)
This is the video I used (x).
So, create your first gif and crop it so that it’s 150px x 150px (x). Sharpen it, color it and do whatever you want until you’re satisfied.
If you want to add the white border on the gif create a new layer (x) and put it on the top of all the layers.
Now select the Rectangular Marquee Tool (M) and draw a square leaving some space from the borders of the gif.
Right click on the image and hit SELECT INVERSE. You should have something like this:
Select the Brush Tool, choose the color white (ffffff) and paint the selection. Then set the opacity of the layer to 20 - 30%.
Save your Gif as you usually do.
Create the second gif (THE TWO GIFS MUST HAVE THE SAME AMOUNT OF FRAMES AND THE SAME DURATION), crop it so it’s like 245px x 245px, sharpen it, color it until you’re satisfied. Then Save it as you usually do.
Now open the two gifs you saved in Photoshop, select ALL THE FRAMES of the 150px gif, click the little arrow on the right and click on Copy Frames.
Select all the frames of the 245px gif, click the little arrow on the right, hit Paste Frames and choose PASTE OVER SELECTION.
If you want to move the 150px gif you have to select ALL the frames of the gif and ONLY the layers of the gif you’ve just pasted.
Move the gif until you’re satisfied and then save it as you usually do.