This method may not be pretty, but for crude servo control with the ATtiny chip, this method should work. I programmed it using an Arduino Uno as shown here.
Hobby servos work by taking the length of time a pulse of electricity is sent to the “signal” input. If it is 1.5 milliseconds (ms), it moves to the middle of it’s travel, 2 ms to the right, and 1 ms to the left. This excellent paper illustrates this, as well as some standard connector colors, which have helped me with some of my projects.
For my “tiny useless machine,” I needed a way to control a servo using the ATtiny chip. Accuracy didn’t have to be great, so what I did was used the delay command to make the pulse either 1 millisecond (delay 1) or 2 milliseconds (delay 2). The code below will show what I mean,