These people are explaining it well, but the things that helps the most to me is consciously de-coupling your internalized knowledge of human Numbers from what they actually represent abstractly. The numbers represent an absolute quantity.

0 =

1 = .

2 = . .

3 = . . .

That's 4 unique characters representing incremental quantities.

If you notice on the comic, the alien has 4 digits on it's "hands". That's the root cause for their base number system. Ours is that way because we we have 10 digits on our hands (most of the time, some cultures do it different, but for simplicity, that's what the comic is implying).

Abstractly, adding another digit represents starting over and keeping track of how many times you've done that. So the 1 in ten says you've counted through all the digits 1 time. And the 0 means you're on the first digit of the new sequence. So all they are doing is applying that logic to a base 4 system. So a collection of 4 things is therefore represented by "one zero," 10, in base 4 because they have to, there are no more characters in that system that could do that by itself.

The weird part about it that can trip people up is that they are applying some human conventions to the comic like our script for writing numbers, which obviously an alien wouldn't do, but we have so much inherent ingrained knowledge about what a number means that it's hard to remember that.