I decided to study Euclid for fun. I have Oliver Bryne's edition.
I also want, as much as possible, to construct the figures myself, to get a deeper understanding. How did people traditionally do this?
I have a compass, and a ruler. So far I've constructed the first three propositions from book one.
However, it's not clear to me how I ought to draw the fourth proposition, or whether it's only meant to be understood.
The later propositions use the earlier propositions where equal line lengths were drawn using circles. If I want to use those same deductions to construct later propositions, should I simply copy the line length with a ruler?
Surprisingly, google didn't turn up much guidance for this project. I'm assuming earlier generations of pupils would have drawn Euclid, no?
An actual compass and straightedge are not needed at all, but it can be fun and educational to use them. You can remember the constructions better when you actually do them. I remember when I constructed a regular pentagon on my front lawn with ropes and drew the lines with lime.
Most of Euclid's propositions aren't constructions, but use them at the beginning to add auxiliary lines needed later to prove the statement of the proposition.
An exception is proposition I.4 that you mention. There is no construction. At most there's a mental motion of one triangle to fit over another. (Euclid's proof is not convincing.)
You ask about transferring lengths with a ruler. The alternative is to use I.3 that you've already done every time you want to copy the length. That's enough justification to copy the length.
It's possible that I.3 wasn't in the original Elements. Earlier Elements might have assumed that lengths could be transferred, and Euclid, or someone else, discovered the construction in I.3 that allowed this operation. That would reduce the assumed constructions (postulates) to the simpler postulate that a circle could be drawn given a center and a point to be on the circumference of the circle.