Gluing small plastic parts back together is a two-part challenge: First you have to find a suitable glue, and then you have to find a way to hold the pieces together while the glue cures.
Challenging need not be impossible though.
If you know what kind of plastic the part you’re trying to glue is made of, and can get a specialty glue for it, that’s your best bet. For example, if the part is polystyrene or a close relative, Testors Liquid Cement is extremely effective. If you don’t know what kind of plastic it is, Surehold Plastic Surgery is more likely to work than anything else.
The other thing you’re going to need is some polymer clay. In a pinch you could use Silly Putty as a substitute.
Press the larger part into the clay. Scrape away a bit of the clay right next to where the other part has to go. You want a clean glue joint.
Next, be ready to work fast. You’ll have to apply some glue to the other piece, then press it into the clay next to the other part. You’ll probably only have a few seconds to make sure everything lines up. You can practice without glue if you’d like.
Once you’ve applied the glue, let it set up overnight, or better yet, for 24 hours. After the time has passed, peel the clay off the part. If all went well, you’ll have a lasting repair.