'dragon from egg to end thing' is that the one where you create a dragon?
anyway, if i understand you right, you're looking for your guardian dragon and be able to bind it to a ring you can summon it with. doesn't work that way, but whatever. guardian dragons are normally young dragons that stay in your house making sure unwelcome guests [spirits, faeries, people] leave, or only stay for a little while. they can also help you with your spell casting, but for the most part, they're like owning a hyper puppy. you'll know your guardian dragon is there typically by sensing them, or having things randomly get knocked over.
there is a ceremony you can do to call to your guardian dragon if you haven't met him/her yet, takes about a month. they come when they feel like it actually, you could try calling to them, there's some chants you could use, but it takes times and patience. same goes for your guide dragon.
try sensing the dragon. depending on the type, say a fire dragon, the room will feel hotter. while walking along, you might feel something brush past you, or hear something.
try sitting quietly and try to sense anything. or, if you're doing that egg thing [not sure what you mean] you could place your hands over the egg, not touching it, and see if it feels warm, or if you can feel movement, or something like that.
binding a dragon to a ring... not sure how well that would go, but my guess is bad.