If you're looking for a quick and easy way to finish fabric edges without sewing, there are several ways you can do it. One popular method is using fusible webbing. This is a paper-backed adhesive that comes in various widths and can be found at most craft stores.
To use this method, simply cut a strip of fusible webbing the same width as your fabric edge. Then, iron the webbing onto the wrong side of the fabric following the manufacturer's instructions. Next, fold the fabric over so that the raw edge is hidden inside and iron again to fuse the two layers together.
Another option for sealing fabric edges is using fray check or a similar product. This is applied directly to the raw edge of the fabric and dries clear, preventing fraying while still allowing you to sew through it if needed.
Finally, if you're looking for a more permanent solution, you can always serge or zigzag stitch around the raw edge of your fabric before washing and drying it according to your project's instructions. This will create a finished look that will withstand repeated washings and wearings.