You can use JavaFX in Swing applications via the JFXPanel control. See the SwingInterOp sample. You can also utilize JavaFX from inside sophisticated Swing based platforms such as NetBeans RCP.
A current limitation of JavaFX/Swing integration is that you can embed JavaFX components in a Swing application, but not Swing components in a JavaFX application. RT-12100 Swing in JavaFX embedding support is currently scheduled for Java 8.
If you have a green field new application to develop, I'd advise choosing one technology or the other and sticking with that or at least keeping the integration points localized and few and far between. Both frameworks are large and take time to learn, plus you will avoid any integration headaches such as needing to take care that Swing processing is done on the Swing Event Dispatch thread and JavaFX processing is done on the JavaFX Application Thread.
JavaFX also integrates with SWT and that integration is currently simpler than the JavaFX/Swing integration (because there is only a single GUI thread to worry about).
Here is a screenshot of JavaFX/Swing interop sample from Oracle:

I went over a few answers on SO with regards to which one to use and I still can not make up my mind.
Rather than doing that, I'd advise picking a small application and implementing it from scratch in Swing and JavaFX and seeing which you prefer. It's time better spent as there is no substitute for hands on experience - then, if you still have questions (hopefully more specific and targeted), come back to StackOverflow to research or ask them.