Your first objective is to get inside the Neighbor's house. Start by observing the house from your yard. The front door is usually locked, and the Neighbor patrols the front. Look for alternative entry points. A common method is to find a window on the ground floor. Often, a window on the side or back of the house will be slightly ajar or can be broken with a thrown object. You can find rocks or bricks scattered around your yard or the Neighbor's yard. Pick one up (Left Click) and throw it (Right Click) at a window. Once a window is broken, you can crouch (Ctrl/C) and enter. Be quick, as the sound of breaking glass will alert the Neighbor.
Another approach is to use the open window on the second floor, often accessible via a stack of boxes or a strategically placed trash can. Drag these objects (Left Click and hold) to create a makeshift ramp. Remember to be stealthy; the Neighbor has excellent hearing and vision, especially in Act 1 where his AI is still learning your patterns.