How can I increase To The Moon's default resolution?

There is no way to customise the resolution, you have two options really - windowed mode in a 640x480 window or fullscreen mode (by toggling it with ALT+ENTER) which will stretch the image to the size of your desktop resolution.

This means that one option could be to change your desktop resolution to the resolution you wish to run the game at and then run it fullscreen, but if you have a monitor with an aspect ratio other than 4:3 then you'll experience blurring and scaling (so the moon won't be round, etc).

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When running in windowed mode, you could use the magnifier (windows key and +) to enlarge the screen.

Press F1 and select Reduce screen flickering for a better experience.

Loads of technical information about the game on this page.