Save your project before you begin your capture. If you haven't created a folder on the hard drive for the project you can create one in the save dialog box.

Once you are ready to begin capturing your video click on File > Log and Capture in the menu:

Log and Capture window:

Click on the Clip Settings tab and make sure that Video and Audio are both checked. If you want to listen to the audio while capturing, then check the Preview box as well.

The Capture Now screen:

Hit 'esc' on your keyboard to stop recording. The clip you have just captured can be found in the Browser window of the Final Cut Pro workspace.

Double click on the clip in the Browser and you will see a preview in the Viewer window.

Set the In and Out points to mark the start and end of your clip. Move the playhead in the Viewer timeline to where you want the clip to begin and hit the Mark In button in the toolbar (or hit the "i" key on the keyboard). Drag the playhead to where you want the clip to end and hit the Mark Out button in the toolbar (or hit the "o" key).

Once you have set your In and Out points you are ready to add your clip to the Sequence. Click and drag the clip from the Viewer window to the Canvas window, and you will see a panel pop up on the right side of the Canvas Window. Drag the clip to the Overwrite box in this pop up: