The general rule is: your report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you worked in and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state. You will have to file a non resident PA state return and pay PA tax on the income earned there.

Since FL does not have an income tax, you do not have a resident return to file.  So, there will be no offsetting credit for the PA tax paid. 

The question you didn't ask is "will PA consider you a resident for tax purposes?"  That depends on the circumstances of how and why you are working there but consider yourself a FL resident. See https://www.revenue.pa.gov/FormsandPublications/FormsforIndividuals/PIT/Documents/rev-611.pdf

Just to clarify, the income you earned from work you carried out in PA is 100% taxable by PA, regardless of whether you are a non-resident or a statutory resident of PA.

The reference provided by @Hal_Al explains "statutory" residency.

There is no "double taxation" because Florida has no income tax.