To get her comfortable pottying on a leash, just keep taking her out on a leash. Eventually, she will HAVE to go. When that happens, tell her how wonderfully fantastic she is, and giver her some super yummy treats (make sure you take the treats out with you).
If you absolutely have to tie her out on a chain, make sure that it is light, and use a harness, not a collar. Also, don't leave her out along for long, and check on her frequently whenever she is tied to make sure she isn't tangled and can reach shelter and water.
If you can't fence the entire yard, at least look into putting up a kennel run. A 10' x 10' pen is plenty large for a young puppy. Again, if you are going to leave her out in it for any length of time, make sure she has shelter from the weather, access to water, and that there aren't any gaps at the bottom that she could squeeze through.