Hi Alex,
If you want to display a report as part of your custom UI, you can create a UI element with type URL and set it to:
~/CMSModules/Reporting/Tools/Report_View.aspx?reportid=
You need to specify the report ID, therefore if you need this to be set dynamically, you can also use macros.
Another approach would be creating a custom aspx page, where you can use any controls as needed and handle everything on your own and then use it as the UI element.