I'm new at developing of Gmail Contextual Gadget, and I want just test my gadget, but I can't find how to do that. As I understand I need to have domain at Google Apps and lot more things, Is there any other solution ? And can I add my contextual gadget to regular gmail account, or I need something else ?
Yes - you are going to need a business account. Your standard Gmail Account won't allow for Contextual Gadgets.
You can pay to get access for 1 user for a year. You can then use that for your testing.
You will need to have a domain to associate with your account but you can pick one of those up at say godaddy for a few dollars.
Although it sounds like a hassle, if you follow the setup steps and are willing to pay the small cost it won't take too long.