How long will my baby bird live with a hole in its head and how should i take care of it?

If you can't take it to a rehabilitation facility, you should really put it out of its misery. The chances for a healthy baby bird being rehabed by somebody with little experience is very low, and with an injury like this, I can almost guarantee that he wont survive. I'm really sorry that thats probably the only thing you can do, but you have the chance to do it in a humane way. My recommendation (if its still a small bird) would be to place him in a freezer bag and try to press out as much air as possible, then place him gently in your freezer. This is how a vet told me to put rescued baby bunnies to sleep, and apparently its the most peaceful at-home method for euthanasia. I'm really sorry, but thats probably the kindest thing you can do for it now.