What are some specific examples of change in governmental structure over the time of the Founding Era (1763-1815)?

There were two major ways in which the structure of
government changed during this time period.

First of all,
there was the change that occurred as the colonies became states in an independent
nation.  The major change here was in the fact that more state officials (as compared to
colonial officials) were elected by the people.  In colonial times, both the governor
and the upper house of the legislature were typically appointed by the Crown.  After
independence, all parts of state governments were usually
elected.

Second, there was the change in the structure of
the national government that came about with the writing and ratification of the
Constitution.  Under the Articles of Confederation, there was really no executive branch
to speak of and the national government had very little power relative to the states. 
Under the Constitution, there was a separate and relatively power executive branch as
well as a judicial branch.  (I should mention as well that the Congress under the
Articles was unicameral where the Congress that the Constitution set up is bicameral.) 
The new national government was also given more power.  For example, it had the power to
impose taxes on the states and to regulate interstate
commerce.

These are the most important changes in
governmental structure during the time that you are asking
about.