Before going directly to Union Bank, you should first sign up their online application form which you can click here: Eon Card Application. Sign up the required fields and you will be given a number which you will present upon going to your nearest Union Bank branch.
The requirements in applying for EON card is photocopies of 2 valid ID's basically government issued ID's. They will also collect 350 pesos for the annual fee of the card. I would suggest that you bring around 500 and deposit the other 150 if you have plans to use the card to verify your Paypal account. If there are few people and there are no problems regarding your application, you may have your card in about less than an hour.
* Upon receiving your card, you will be needing to enroll it on Eon Card's site. You will be needed to make a username for your card. Make sure you remember your username and your pin number in order to log in your account.
* If you have lost your card, Report to your bank and ask for a replacement. Bring some money because they charge for replacement of cards.