This is something that we need to plan a bit before we start working on any artwork. The most basic factor that decides on canvas size is the target.
Web or Print?
If you are planning the artwork to be used for web or onscreen media, then 90 dpi should be sufficient in terms of resolution. As a matter of fact, you need not worry that much about dpi and just measure things in pixel.
On the other hand, if you are intending to create prints of your artwork, then you have to ask yourself how large, physically, do you need the artwork to be printed. Get that physical dimensions in terms of inches, and then multiply it by 300. That way you would get a 300 dpi resolution.
In any case, when you are working on a digital painting, use a size 10% to 20% larger than the required size. It is much easier to crop or scale the image at the final stage, and more importantly, it is easier to work on larger resolutions. It will be like you are wearing a magnifiying glass.
What is dpi?
It expands to – dots per inch. When you print an artwork, each pixel would be considered as a dot, and it will squeeze 300 of those pixels into an inch. The screen resolutions are much lower and if you are going to target screen, then you can aim at 90 dpi.
To be on the safer side, I always work at 300 dpi. If I need to put a screen version, I just scale it down.
So, what will the resolution be for a post-card size print?
Assuming that a post card size is 5.6″x4.25″ and we need to print it at 300 dpi, we get the resolution as 1680×1275 pixels.
For other sizes, simply multiply the number of inches by the dpi value.