Pixels are the only dimension that matters
An image has one real size: its pixel dimensions. The DPI or PPI figure stored alongside is metadata used by print software to decide how large to lay the image out on paper, and it has no effect whatsoever on a screen. Changing it without changing the pixel count changes nothing about the file.
This is why the advice to 'save at 72 DPI for web' is a myth that refuses to die. A 1200×800 image is 1200×800 whether it claims 72 or 300 DPI. What matters for print is the ratio: 1200 pixels across a 4-inch print is 300 pixels per inch, and that arithmetic is where the number becomes real.
Keep the aspect ratio unless you mean not to
Set one dimension and let the other follow. The lock is on by default here because stretching an image to fit a shape is immediately obvious to a viewer even when they cannot say why — faces widen, circles become ovals, and text leans.
When a target shape genuinely differs from the source, crop rather than stretch. Cropping discards the parts you do not need and leaves the rest correctly proportioned, which is what every platform's own image tool does when it fits your photo to a banner.
Downscaling is safe, upscaling is not
Making an image smaller averages existing pixels together and generally improves apparent sharpness, because noise and compression artifacts average out along with everything else. There is no quality penalty worth worrying about.
Enlarging has to invent pixels that were never captured. Interpolation produces a smooth, soft result rather than new detail — the missing information does not exist anywhere in the file. Beyond roughly 150% of the original, the softness becomes obvious. Going back to the original source at a higher resolution is the only real fix.
Common target sizes
For a website, match the largest size the image will actually be displayed at, then double it if it must stay crisp on high-density screens — a 600-pixel column wants a 1200-pixel image and no more. Anything beyond that is bandwidth spent on pixels the browser throws away.
For documents and forms, the requirement is usually stated in pixels or in file size, and the two interact: reducing dimensions is the fastest way to meet a size cap without touching quality. For print, work from the physical size and 300 pixels per inch — a 6×4 inch photo needs 1800×1200 pixels.