how to fit object according to screen resolution in javaFX

There are numerous ways to do that.

If you only care about the height of the nodes (button , labels) , then use a VBox and set the components'  vgrow to always.

VBox.setVgrow(button1, Priority.ALWAYS);

On the other hand, if you care about width, use a HBox and set the components'  hgrow to always.

If you want both of width and height of the nodes to fit to the screen, then you can :

1.      Use a gridpane. GridPane will resize the nodes of the screen according to screen size.
2.      Use a VBox inside an AncorPane and set the constraints to 0 , minSize to 0 , maxSize to Double.MAXVALUE like this:

<?xml version="1.0" encoding="UTF-8"?><?import javafx.scene.control.*?>
<?import java.lang.*?>
<?import javafx.scene.layout.*?>
<AnchorPane maxHeight="-Infinity" maxWidth="-Infinity" minHeight="-Infinity" minWidth="-Infinity" xmlns="http://javafx.com/javafx/8" xmlns:fx="http://javafx.com/fxml/1">
   <children>
      <VBox layoutX="53.0" layoutY="25.0" maxHeight="1.7976931348623157E308" maxWidth="1.7976931348623157E308" spacing="10.0" AnchorPane.bottomAnchor="0.0" AnchorPane.leftAnchor="0.0" AnchorPane.rightAnchor="0.0" AnchorPane.topAnchor="0.0">
         <children>
            <Button maxHeight="1.7976931348623157E308" maxWidth="1.7976931348623157E308" minHeight="0.0" minWidth="0.0" mnemonicParsing="false" prefHeight="41.0" prefWidth="458.0" text="Button" VBox.vgrow="ALWAYS" />
            <Button maxHeight="1.7976931348623157E308" maxWidth="1.7976931348623157E308" minHeight="0.0" minWidth="0.0" mnemonicParsing="false" prefHeight="41.0" prefWidth="458.0" text="Button" VBox.vgrow="ALWAYS" />
            <Button maxHeight="1.7976931348623157E308" maxWidth="1.7976931348623157E308" minHeight="0.0" minWidth="0.0" mnemonicParsing="false" prefHeight="41.0" prefWidth="458.0" text="Button" VBox.vgrow="ALWAYS" />
            <Button maxHeight="1.7976931348623157E308" maxWidth="1.7976931348623157E308" minHeight="0.0" minWidth="0.0" mnemonicParsing="false" prefHeight="41.0" prefWidth="458.0" text="Button" VBox.vgrow="ALWAYS" />
            <Button maxHeight="1.7976931348623157E308" maxWidth="1.7976931348623157E308" minHeight="0.0" minWidth="0.0" mnemonicParsing="false" prefHeight="41.0" prefWidth="458.0" text="Button" VBox.vgrow="ALWAYS" />
            <Button maxHeight="1.7976931348623157E308" maxWidth="1.7976931348623157E308" minHeight="0.0" minWidth="0.0" mnemonicParsing="false" prefHeight="41.0" prefWidth="458.0" text="Button" VBox.vgrow="ALWAYS" />
            <Button maxHeight="1.7976931348623157E308" maxWidth="1.7976931348623157E308" minHeight="0.0" minWidth="0.0" mnemonicParsing="false" prefHeight="41.0" prefWidth="458.0" text="Button" VBox.vgrow="ALWAYS" />
         </children>
      </VBox>
   </children>
</AnchorPane>

I suggest you to use the scene builder to test different possible cases and choose one that fits your application.

In scene builder, I set the Min Width and Min Height to USE_COMPUTED_SIZE and this works fine.