This is an actual screenshot from the title screen of The Secret of Monkey Island (DOS, 1990):

As you can see (by downloading the image file and inspecting its properties), it's 320 × 200 pixels. As you can also see, it looks very tiny on a modern screen, and also slightly flattened vertically (although that's kind of hard to tell at a glance in this case).
This is what it would've (approximately) looked like on an actual VGA monitor in 1990:

That's the same screenshot, but rescaled to 1600 × 1200 px. When viewing it inline here in this answer, your browser may rescale it back down to fit the Stack Exchange column width, but it should maintain the 4:3 aspect ratio.
Only that's not really historically accurate either, because this is more like what it would've really looked like on an actual CRT VGA monitor:

This is the same rescaled image as above, but with some blur and a layer mask (generated using the "linear sinusoid" effect in GIMP) applied to simulate the scanlines and color mask of a CRT screen. Specifically, there are exactly 400 horizontal scanlines (because VGA used scan doubling in low resolution modes) at 3 px per scanline, plus a subtler pattern of 640 vertical lines to mimic the CRT color mask.
The difference is honestly kind of subtle, especially with the VGA scan doubling, but it does make the rescaled image look subtly nicer in several ways. Probably the most obvious difference is with the town lights on the bottom left, which now look nice and glowy instead of just a mess of blocky pixels. The text also looks smoother, the stars are less blocky and the dithering pattern in the sky gradient is less distracting. That's all because this is (closer to) how these VGA pixel graphics were originally meant to be viewed.
(The image with the simulated CRT effect also looks noticeably darker than the previous image, but that's not intentional, but just an unavoidable side effect of the applying the scanline mask. You can adjust you monitor brightness up to compensate for it.)
So, if you want to mimic the appearance of these 1990s VGA games, what should you do?
First, if you already have a high-resolution picture that you'd like to "convert to VGA", then I'd recommend:
- cropping it to a 4:3 aspect ratio,
- rescaling it (non-uniformly!) to 320 × 200 pixels, and
- if desired, quantizing it to a palette of 256 colors (with 6 bits per RGB color channel, if you really want full historical accuracy).
On the other hand, if you're manually drawing the art pixel by pixel (which is how these kinds of pictures would've historically been created, or at least given the finishing touches), then I'd recommend working directly on a 320 × 200 pixel canvas — preferably using a pixel art editor than can display the image rescaled to a 4:3 aspect ratio while you edit it.
Finally, if you want to show these pictures the way they would've looked on a 1990s VGA monitor, then I'd recommend doing something like what I demonstrated with the Monkey Island screenshot above (i.e. scale to e.g. 1600 × 1200 px and apply a simulated CRT effect). Or, alternatively, getting your hands on an actual CRT from the 1990s.