The Paint editor here can give a picture a see-through background directly. A new picture starts out covered by the secondary color, which is white unless changed, so the work comes down to two things: telling the editor that the picture may have see-through pixels, and then removing the parts you don't want. The file you save is a PNG, which holds on to the transparency.
Switch the picture to Transparent in Image Attributes
When you start a new picture, it is opaque and filled with white, the default secondary color. The setting that controls this lives in Image > Attributes..., which you can also open with Ctrl+E. The dialog has a Transparency group with two choices, Transparent and Opaque, and it always shows which one the picture is using right now. Picking Transparent does not wipe the white away by itself. It only lets the tools that remove pixels leave real see-through areas behind instead of refilling them with color.
- Open Image > Attributes... or press Ctrl+E.
- In the Transparency group, choose Transparent.
- Press Okay.
Erase the white background to clear pixels
Once Transparent is on, the Eraser no longer lays down color. Dragging it with the left mouse button turns the pixels under it fully see-through. If Opaque is still chosen, the same strokes simply leave patches of the secondary color. Check the setting first if the background stays white.
- Make sure Transparent is chosen in Image > Attributes... and press Okay.
- Choose the Eraser/Color Eraser tool.
- Hold the left mouse button and drag across the background areas you want gone.
- Use File > Save to download the result as a PNG.
Start from a fully clear canvas or add clear space
Sometimes it is easier to begin with nothing at all and draw on an empty, see-through canvas. With Transparent turned on, a few other actions also leave clear pixels instead of colored ones:
- Image > Clear Image (Ctrl+Shift+N) empties the entire picture to transparent.
- Making the picture bigger, either in Image > Attributes... or by dragging the canvas handles, adds new area that is transparent.
- Rotating by an angle that is not a right angle leaves the empty corners transparent.
- File > New gives the new picture a secondary-color fill, but it keeps whatever Transparency choice you made, so Clear Image right after it gives you a blank, clear canvas.
Place a cutout over another picture with a transparent selection
A different method is to cut a subject out and drop it onto another picture so its background color disappears. Three tools carry an Opaque and a Transparent option: Select, Free-Form Select and Text. With Transparent chosen, any pixel in the selection or text that matches the current secondary color turns see-through as you drag the selection or type the text, so whatever is underneath shows through. Image > Draw Opaque is a checkbox that toggles this same option. This works on its own and does not change the picture's Transparency setting in Image > Attributes....
- Open the picture that holds the subject.
- Make the background color you want to drop the secondary color: right-click it in the color box, or choose Pick Color and click the background with the right mouse button.
- Choose Free-Form Select, then click Transparent in the options area under the tool box.
- Hold the left mouse button and trace around the subject.
- Press Ctrl+C to copy the selection (or Ctrl+X to cut it), open the other picture and press Ctrl+V. In a browser, the Edit menu entries for these may be greyed out, so the keys are the reliable route.
- Drag the pasted selection into place; the parts that match the secondary color let the picture below show through. Keep Transparent chosen while you do this.
Save the image as a PNG that keeps transparency
There is no format menu to worry about. File > Save and File > Save As always download a PNG file, and PNG stores the see-through pixels along with the rest of the picture. The autosave in your browser also keeps the picture as PNG, so a clear background survives a reload. To save only a piece of the drawing, select it and use Edit > Copy To..., which downloads the selection as selection.png.
Open a picture that already has a clear background
You don't need to set anything when you load a PNG that is already partly transparent. As a picture opens, the editor looks at each of its pixels, and if even one is not fully opaque, the editor switches it to Transparent for you. The same check happens when you open a file, drag a file onto the page, load a picture from a URL or get back an autosaved picture. A picture with no see-through pixels at all opens as Opaque.
Work with colors and turn transparency back off
The color box has no see-through swatch, so you can't paint transparency on with a brush. Clear areas come only from erasing, clearing the image, enlarging the canvas, rotating by an angle that is not a right angle, or loading a picture that already has them. Pick Color does keep the transparency of the pixel you click, though. If you want a solid background again, open Image > Attributes..., choose Opaque and press Okay: every transparent pixel turns the secondary color, and the Eraser, Clear Image and canvas enlarging go back to using that color too.