Instructions
Open "Buy Mode" and purchase a telescope for your Sim's house. The more expensive the telescope, the better chance you have of encountering an alien while using it. Place the telescope outside your Sim's home. It will not work indoors.
Fulfill your Sim's needs like Hygiene, Hunger and Bladder before looking for aliens. Your Sim will need to use the telescope for long periods of time without interruption, so try to make sure all of his bars are in the green before proceeding.
Click on the telescope and select "Stargaze." Your Sim will start gazing through the telescope. Continue stargazing between 7 p.m. and 2 a.m. without stopping. Your chances of encountering an alien are better the longer you stargaze without taking a break.
Stargaze every night until the alien spaceship visits your home and abducts your Sim. The chances of being abducted are slim, so you will likely need to perform this task nightly Sim is contacted by aliens.