How to fix the wire connections on three-way switches?
The source goes to the black screw, yes.  But both brass screws are travelers.  What's always true with travelers is 


There are two of them
They are interchangeable 
They are in the same cable on both ends 
They are the same colors on both ends (obviously) 
On both 3-ways, the two travelers go to the two brass screws


So for instance the travelers might be the red and white.  It really depends on what your installer picked for each segment of cable run, and some installers choose different colors for each segment. 

Now, I greatly simplify my life by marking both travelers with yellow tape. And anytime you mark a wire with tape, mark both ends of the wire.  

Now the first 3-way is super simple, both "yellow" wires are landed on both brass terminals.  Assuming the cable run is continuous between the 3-way switches, the other two travelers are also marked yellow and go on the brass screws there.