We are married. I live in Florida and she lives in Virginia and have both personal and joint assets. How to file Federal and respective state returns?

Try the link below. I hope it's of some utility.

https://ttlc.intuit.com/turbotax-support/en-us/help-article/small-business-processes/prepare-joint-federal-return-separate-state/L7I53364c_US_en_US

Virginia's filing rules are a bit complicated when one spouse is a VA resident and the other is not.  See Filing Status on page 9 of the VA tax instruction booklet:

https://www.tax.virginia.gov/sites/default/files/vatax-pdf/2022-760-instructions.pdf

Florida, of course, has no personal income tax.

For most married couples, filing a joint federal return is best.  

As noted by @TomD8, the rules get cumbersome with facts such as yours.

The rules are explained in the instructions to both the form 760 and 763.

In reading those rules, there are too many unanswered questions for someone on this forum to provide an accurate response.

You will need to review the rules and determine your options and then run the numbers to determine which filing method is best based on your specific facts.

Consulting  with a VA tax professional may be in order to provide some direction / advice.