I need to add some functionality (sending email) to my portlets. I want to do it with ext-plugin and use <portlet:actionURL ...> in my jsp-pages. How implement this action with ext-plugin?
You don't want to use ext-plugin: It's invasive and you get access to the implementation details of Liferay that you might inadvertently use and become dependent upon.
So if it's your own portlets, do yourself a favour and implement them in a proper plugin. Note that portlet support is deprecated in ext-plugins and will be removed from later versions: You might as well do the shift now and stop using ext for portlets already.
To clarify, because I said you don't want to use ext: You might need to use ext, and ext is a wonderful mechanism to override lots of Liferay's implementations - works well and has long been established. However, it's invasive and it results in more upgrade difficulties than other - properly separated - plugins. But, even if you need to use ext: Keep it as small as possible and do the bulk of your work outside of it, in plugins.
Now for your question:
I have the impression that you already have portlets (as you want to add something to them) and don't understand what you're asking: Is it "How do I send mail in java?" or "How do I program to the portlet API?" or "How do I use Liferay's services to send EMail?"
The first two questions are a bit too broad for answering in this context, for the third you might want to look at Liferay's MailLocalServiceUtil class, available to plugins as well.