If you're having an issue with gaining an animal follower, make absolutely certain you have completed any quest with an animal follower or that you haven't accidentally left one behind, elsewhere in a previous quest.
Dogs (specifically adopted dogs) in Skyrim have a known bug which may also create your issue:
...Certain dogs can also be recruited as potential followers
throughout the game. You can have at most one canine follower at any
time. If your dog is left waiting for too long, a message will appear
stating that it has grown tired of waiting and will start walking to
their original location...
...A dog companion told to go home will go home to its own original home,
or your first encounter area, not any of your homes. This appears to
have been the intended behavior, unless it was adopted by your
If a dog follower gets adopted by your children, it may wander off to
the wrong house. This seems to happen when dismissed outdoors and when
your family lives in one of the three homes added by Hearthfire. It
may also happen if the dog is already adopted and you move the family
to one of the Hearthfire homes.
To resolve this, find the dog and ask it to follow you, walk home, go
indoors, and tell it to wait there. Even after two game days pass, it
will still be there. Dismissing the dog in the house might also work.
PC users can find the dog by using the console command
<dog id>, but even without it you should find the dog wandering
around near one of the other homes.
The above fix however, is for the PC version.
You may fix the issue on console in a more tedious fashion by going back and retracing steps to locate a forgotten or stuck animal.
Another fix is the trick to wait X days (typically three). Followers often consider this time frame "too long" to wait around and automatically leave to whence they came. This doesn't always work but is the least tedious method of attempting to fix the issue.