  It is well-known that the constructions of space-filling curves depend on
certain substitution rules. For a given self-similar set, finding such rules is
somehow mysterious, and it is the main concern of the present paper. Our first
idea is to introduce the notion of skeleton for a self-similar set. Then, from
a skeleton, we construct several graphs, define edge-to-trail substitution
rules, and explore conditions ensuring the rules lead to space-filling curves.
Thirdly, we summarize the classical constructions of the space-filling curves
into two classes: the traveling-trail class and the positive Euler-tour class.
Finally, we propose a general Euler-tour method, using which we show that if a
self-similar set satisfies the open set condition and possesses a skeleton,
then space-filling curves can be constructed. Especially, all connected
self-similar sets of finite type fall into this class. Our study actually
provides an algorithm to construct space-filling curves of self-similar sets.
