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These are free, open-source programs that you can use to create vector images from JPG files. GIMP is an image editor similar to Photoshop, and Inkscape is a vector graphics editor like Illustrator. Both are available for all operating systems.  You can download GIMP from gimp.org. Run the installer for your operating system and leave the settings at their defaults. You can download Inkscape from inkscape.org. Run the installer for your operating system and leave the settings at their defaults. This method is only suitable for simple images with basic colors, like logos and emblems. Converting high-detail images will take a lot of work smoothing rough edges and getting good colors. Use the selection tool to create a rough border for your image. This will make recoloring it easier. This will remove everything except what you've selected. This will tighten up your selection. Once you've finished cropping the file, you can export it. Click the File menu and select "Export As." Leave the settings at their default and give the file a name so that you know it's the cropped version. After exporting the file, open it in Inkscape. You'll see it appear in your Inkscape workspace. You'll need to select the image before you can trace it in Inkscape. This will open the Trace Bitmap window. This will display a preview of what the vector image will look like with that vectorization method. The "Colors" option will give you the closest approximation of the original image. You can adjust some settings for most of the presets. Click "Update" after each settings change to see the results. The original image will be traced and replaced with the vector image. This tool will allow you to select areas of the vector image and then drag nodes to adjust the size and shade. Click a part of your images and you'll see a bunch of small boxes appear. Drag these boxes to change the shapes for your selection. During the trace, some parts of the image may have been connected when they shouldn't have been. The Break Paths tool allows you to separate these parts by removing connecting nodes. Once you're satisfied with your vector image, you can save it as a vector format.  Click the File menu and select "Save As." Select a vector format from the "Save as type" menu. Common formats include SVG (for websites) and PDF (for print). Save a copy as an Inkscape SVG to be able to go back and make easy edits.
Download and install GIMP and Inkscape. Open GIMP and use the Rectangle Select tool to select the part of the image that you want to convert to vector. Click the "Image" menu and select "Crop to Selection." Click the "Image" menu again and select "Autocrop." Export the file. Load the file in Inkscape. Click the image to select it. Click "Path" and select "Trace Bitmap." Select the different methods and click the "Update" button. Adjust the settings for the preset methods. Click "OK" when you're satisfied with the results. Use the "Edit paths by nodes" tool to make fine adjustments. Use the "Break Path" tool to separate nodes that shouldn't be connected. Save your image as a vector file when you're finished.