There are several companies that provide cellular and satellite phone rental services, most of which have offices in or near the large, chain hotels. Normally, you are required to pay a daily rental fee in conjunction with a "per minute" usage fee. Most companies require a valid passport and deposit, which can be paid in cash or with a credit card - for an additional fee insurance is available.
For those who would rather purchase a cell phone you can do so in any electronic/cell phone store, or from the cell phone providers themselves - Cable & Wireless or Telefonia Moviestar. There's plenty of competition between the two, so services are quite extensive and reasonably priced. In Panama, you do not pay for incoming calls, just outgoing, and the per-minute usage fee will depend on your provider, the type of pre-paid phone card you purchased, or which contract you have signed.
Using Prepaid Phone Cards
Phone cards come in various denominations, ranging from $5.00 - $20.00. The more expensive the card the less you pay "per-minute" to use the phone. Phone cards can be purchased just about anywhere, and the providers often run 2x1, 3x1 specials.
Annual contracts - cellular phone usage
Foreigners and locals alike can sign a comprehensive contract with a local provider, with foreigners required to make a deposit. Contracts range in prices, as do services, but expect to pay considerably less if you agree to a yearly contract than what you will pay by using a pre-paid phone card.