There are multiple ways to do this.
In construct :
Double click on your sprite, it will open the image editor.
If the background is only filled with 1 color, use the magic wand tool to select it, and then press del.
If there are multiple colors, a drawing, whatever, you'll have to use the eraser tool. Set opacity to 255 so that the erased parts will be 100% transparent. Set the size to whatever you need. You know what to do next.
Close the editor and it will prompt to save.
Or if your image is not in construct, open it with any image editor you like (gimp?) and proceed just as written above. Save the file as .PNG to keep the transparency, then import in construct.