Background. First off, I want to share with you some background about browser add-ins. There are two kinds of add-ins: extensions and plug-ins.
A plug-in involves native executable code that gains much more intimate access to your browser, and is not restricted by any sandbox. For instance, Flash player is a plug-in.
Plug-ins are considerably more dangerous, because they have full access to your filesystem, full access to run programs on your machine, full access to your browser (and all web sites you visit, passwords, etc.); they can do anything you can do. Extensions are more limited in what they can do (at least in Chrome), and thus (in Chrome) are safer.
I suspect you are asking about an extension, not a plug-in. For instance, the extensions in the Chrome Gallery are extensions.
How to tell if it is safe. In general, there is no good way to tell if an extension is safe. You can look at reviews from other users (though this is not fully dispositive). You can look to see if the extension has been around for a while, has a significant number of users, and/or comes from a respected brand/company/developer (though this is only an indicator and certainly not a guarantee of security).
And, perhaps most importantly, in Chrome you can look at the permissions that the extension is requesting. This will tell you what information the extension will gain access to and what it could do, if it were malicious. A malicious extension will be constrained by its permissions, so the fewer the permissions, the lower the risk of the extension.
Further reading. For more information, I suggest that you read the following: