If you plan to stay in Aruba for less than 90 days you need a U.S. passport, a valid return ticket leaving Aruba within 90 days and sufficient funds to support yourself while you are in Aruba. You are not allowed to work.
If you are staying more than 90 days but do not intend to move to Aruba permanently, you need the same items mentioned in section one plus a temporary residence permit. Again, you are not allowed to work or conduct business in Aruba and must be self-sufficient. All forms can be obtained from the Directorate of Alien Integration, Policy and Admission (DIMAS).
If you're moving permanently to Aruba, you will need a permanent residence permit. To obtain one without also obtaining a work permit, you need: a bank statement showing you have funds to support yourself without working, proof of address for the past 10 years, a valid reason for moving to Aruba, and a clear police record for two months previous. In addition you will need a U.S. passport, three passport-sized photos and a clear medical history with smallpox vaccination. You are advised to have your permit before moving rather than apply for it while on the island.
If you plan to work in Aruba, you will also need a work permit. These are not easily obtained because jobs are filled with local Arubans first. Generally, you will need to secure employment before arriving and have the employer file for a work permit for you.