What are the requirements of an HSA? Am I eligible?

You need to have a qualifying High Deductible Health Plan (this essentially means that you have to pay for all covered medical services (except preventative care) before your health insurance kicks in. So no copays or coinsurance before your deductible is met).
Can’t be enrolled in any other non-HSA qualified health insurance plan.
Can’t have or be eligible to use a general purpose Flexible Spending Account (FSA). Limited purpose FSAs are allowed for Dental, Vision, and Dependent Care if your HDHP doesn’t cover those services. Be sure to check with your employer in case this applies to your situation.
Can’t be claimed as a dependent n someone else’s tax return.
Can’t be enrolled in Medicare (Part A and Part B) or Medicaid.