You can do it without a green screen, but you will need to mount your camera solidly, as on a tripod, or very firmly on a table. Take one shot of the background, then, without moving the camera, take another shot with yourself in the picture.
In Vegas, put the clip with you in it onto Track 1, then put the clip of the background onto Track 2. Right click the Track Header to Track 1 and select Insert/Remove Envelope. Select Composite Level, and a blue line will appear at the top of Track 1. Moving this up and down will vary the “transparency” of the event, and can also be keyframed so you can fade in and out if you wish. Provided the camera was not moved or the settings altered between takes, the background should remain in perfect alignment, and the fading in and out should not be noticeable.