I love Aldol. Anyhow, out of your two starting materials, which one has the only enolizable protons? That compound will then perform a nucleophilic attact on the most electrophilic center of the other molecule (where is it?). That's the Aldol addition.
From there, there's a formal removal of water -- the condensation. This leaves behind a double bond.
Do you know what the product looks like? As for cis vs. trans, draw out the transition state and observe.
As for determination by 1H-NMR, yes, you'd measure the coupling constants of the splitting pattern (in Hz). Cis protons will be from 6 to 12 Hz (typically 10 Hz), and trans protons will be from 12 to 18 Hz (typically 17 Hz).