Factory for object init and configuration
I find the right word in you question - 'extract'.

Code style

Logic section

Use blank lines to separate your code into logical sections

Instead of:

DateField dateField = new DateField();
dateField.setCaption(caption);
dateField.setDateFormat(UilibI18N.dateFormat.getText());
dateField.setResolution(Resolution.DAY);
bind(dateField, propertyId);


You can use:

// creation logic part
DateField dateField = new DateField();

// setting the field's properties logic part
dateField.setCaption(caption);
dateField.setDateFormat(UilibI18N.dateFormat.getText());
dateField.setResolution(Resolution.DAY);

// bind operation logic part
bind(dateField, propertyId);


Design issue

I read your code very carefully and I've found that you use 2 variables in all your 3 if/else conditions. 

They are caption and propertyID.

Assume that these 2 properties will be an input of some method which we'll call (I don't know the context, that's why I'll use the random name) makeOperationWithField

public void makeOperationWithField(int propertyID, String caption) {
 // some code
}


I'll move deeply and remove this big if/else if statements.

Replace conditional with polymorphism. 

Lets do it step by step.

Step1 

Create an abstract class that will create objects depending on field's type.

abstract class FieldConfigurationType {
  static final int TEXTFIELD = FieldConfiguration.FIELD_TYPE.TEXTFIELD;
  static final int SEARCHFIELD = FieldConfiguration.FIELD_TYPE.SEARCHFIELD;
  static final int DATEFIELD = FieldConfiguration.FIELD_TYPE.DATEFIELD;

  abstract void makeOperationWithField(int propertyID, String caption);

  public static FieldConfigurationType newType(int code) {
    switch (code) {
      case TEXTFIELD:
        return new TextFieldConfiguration();
      case SEARCHFIELD:
        return new SearchFieldConfiguration();
      case DATEFIELD:
        return new DateFieldConfiguration();
      default:
        throw new IllegalArgumentException("Incorrect Field Type");
    }
  }
}


Now, we can use the simple construction:

FieldConfigurationType fieldType = FieldConfigurationType.newType(type);
fieldType.makeOperationWithField(propertyID, caption);


Step 2

Add separate implementation for each field type.

public class TextFieldConfiguration extends FieldConfigurationType {
  @Override public void makeOperationWithField(int propertyID, String caption) {
    TextField textField = new TextField(caption);
    textField.setNullRepresentation("");

    bind(textField, propertyId);

    field = textField;

    if (field.getValue() == null &amp;&amp; isNestedProperty) {
      ObjectProperty property = new ObjectProperty("", String.class);
        textField.setPropertyDataSource(property);
    }
  }
}

public class SearchFieldConfiguration extends FieldConfigurationType {
  @Override public void makeOperationWithField(int propertyID, String caption) {
    SearchBox searchField = new SearchBox(caption);
    bind(searchField, propertyId);

    field = searchField;
  }
}

public class DateFieldConfiguration extends FieldConfigurationType {
  @Override public void makeOperationWithField(int propertyID, String caption) {
    DateField dateField = new DateField();

    dateField.setCaption(caption);
    dateField.setDateFormat(UilibI18N.dateFormat.getText());
    dateField.setResolution(Resolution.DAY);

    bind(dateField, propertyId);
  }
}


If you need to add a new field type, all you need to do is just add new subclass without rewriting the existing code. Open/Closed Principle