I believe this is an example of Portulacaria afra, sometimes called Baby Jade or Elephant Bush, a succulent related to the more familiar Jade Plant. It is a pretty decent looking specimen and is worth the effort to revive it.
The most important thing is to realize that this plant stores water in its fleshy stems and leaves. Being unaware of this many growers tend to water it too frequently. So, perhaps contrary to your instinct, don't water it at all until the soil dries out completely.
This is a tender plant and cannot be kept outside during the winter but I leave mine outside all summer only bringing them in when temperatures fall into the 40's at night, do not allow them to freeze.
Keep it in a bright location and manage the water appropriately and you stand a good chance of reviving it and having a nice bonsai.