I have been told that it is permissible to walk my dog on a leash even though my entire yard is not fenced in. Another source said you can carry up to 4 cubits (not sure how far that is). Everything would be only on my propery. Please clarify. Thanks.

It is permissable to walk a dog on a leash on Shabbat, even in an area that is not enclosed. One must be careful, however, that the leash does not extend beyond the hand. The part of the leash which is between the man and the dog is considered to be carried by the dog, however if the leash extends over the hand by more than a "tefach" (about 4 inces) that part of the leash is being carried by the person, and that is not permitted.