Since Blender 3.0 (relevant commit)

The UI for a custom property is described by a IDPropertyUIManager that can be retrieved by the id_properties_ui method.

import bpy

context = bpy.context
obj = context.object

# create the property, set it the initial value
if "scale_factor" not in obj:
    obj["scale_factor"] = 1.0

# get or create the UI object for the property
ui = obj.id_properties_ui("scale_factor")
ui.update(description = "Scale factor")
ui.update(default = 1.0)
ui.update(min=0.0, soft_min=0.0)
ui.update(max=10.0, soft_max=10.0)

# test UI in text editor footer

def draw(self, context):
    ob = context.object
    self.layout.prop(ob, '["scale_factor"]')

bpy.types.TEXT_HT_footer.append(draw)

Before Blender 3.0

The UI for a custom property is described by a dict object, stored in a special/hidden _RNA_UI property.

The internal blender addons tend not to access _RNA_UI directly, but use the rna_prop_ui.rna_idprop_ui_prop_get function to get or create the relevent "ui" object.

import bpy

context = bpy.context
obj = context.object

from rna_prop_ui import rna_idprop_ui_prop_get

# create the property, set it the initial value
obj["scale_factor"] = 1.0

# get or create the UI object for the property
ui = rna_idprop_ui_prop_get(obj, "scale_factor", create=True)
ui['description'] = "Scale factor"
ui['default'] = 1.0
ui['min'] = ui['soft_min'] = 0.0
ui['max'] = ui['soft_max'] = 10.0

# test UI in text editor footer

def draw(self, context):
    ob = context.object
    self.layout.prop(ob, '["scale_factor"]')

bpy.types.TEXT_HT_footer.append(draw)
```