The general form is:
convert input.jpg -crop WIDTHxHEIGHT+0+0 result.jpg
If you want to crop to a specific width, say 1024, leaving the height unaffected:
convert image.jpg -crop 1024x+0+0 result.jpg
If you want to crop to a specific height, say 768, leaving the width unaffected - note the height is after the x:
convert image.jpg -crop x768+0+0 result.jpg
If you want to crop to a maximum width and height, say 1024 wide by 768 tall without distorting the aspect ratio:
convert image.jpg -crop 1024x768+0+0 result.jpg
If you want to crop to a specific width and height, say 1024 wide by 768 tall and are happy to allow gross distortions:
convert image.jpg -crop 1024x768+0+0\! result.jpg
Think of the exclamation mark as meaning "just do it!". Note that the backslash is only needed on Linux/Unix/macOS to escape the exclamation mark, you omit the backslash on Windows.
Note, if you are saving the cropped image in PNG format, you probably want to reset the page afterwards so the image "forgets" it used to be part of a larger image:
convert input.jpg -crop 1024x768+0+0 +repage result.png