# I stirred Cyrus up in righteousness

Here the word "righteousness" refers to right action. Possible meanings are 1) that Yahweh has stirred up Cyrus to do the right thing or 2) that Yahweh was right to stir up Cyrus.

# I stirred Cyrus

Yahweh speaks of causing Cyrus to act as if it were stirring him from slumber. 

# I will smooth out all his paths

Yahweh speaks of removing obstacles and causing Cyrus to be successful as if he were making the paths smooth on which Cyrus walks.

# He will build my city

This refers to Jerusalem.

# not for price nor bribe

"he will not do these things for money"