Aliens are all around you on the map! To collect new Aliens, simply capture them once.
Capture the same Aliens on the map again, and you'll receive additional cards for that Alien. Once you collect enough cards, you'll be able to upgrade that Alien in the Database, boosting that Alien's stats. (Note, you will need to spend Credits for each upgrade to the next level.)
You must take into consideration various safety factors when looking for an Alien (i.e., time of day, awareness of your surroundings, and not trespassing). Aliens should all be located in public locations in order to be accessible for all players. If you see an Alien placed in an inappropriate location, tap on the Alien. Then tap on the GPS icon and fill out the Report Issue with Location form. Or contact Player Support.