IntelliJ IDEA does not have built-in profiling capability. There is the VisualVM Launcher plug-in which integrates the free VisualVM tool. VisualVM has been bundled with the JDK since Java 6 update 7. You can download it for earlier versions. VisualVM is a decent, albeit basic, tool. It is good for a beginner and can give you a good general picture of the what is going on in your application, at least if it is running local. A number of features are not available when profiling a remote application. I've only dabbled with VisualVM and have not tried the plug-in for it.
The YourKit Java Profiler is an awesome profiler with lots of features and has great integration with IntelliJ IDEA. The download comes with an IDEA plug-in that allows YourKit to integrate right into IntelliJ IDEA. YourKit is one of, if not the best profilers out there. It is the profiler I use and have been using for the past 4 or 5 years. I also believe it is the profiler the JetBrains developers use themselves (and to me that's a pretty good endorsement for any product). It is a commercial product with a $499 price tag. However they do sometimes offer $99 personal licenses that are advertised in their forums. If there is not a current offer, send an e-mail to their sales department and ask about purchasing a personal license. They will often reply with an offer to sell you one. There is also a 15 day evaluation available.
Lastly there is JProfiler, another commercial profiler . I've never used it, but have some co-workers that do use it and speak well of it. And like YourKit, it has a good reputation in the industry. It has a Plug-in available. It also retails for $499. I do not know if they offer personal licenses.
Those are the profiles I am aware of. Perhaps others know of some more.I hope that helps.