It's a cupressus that lacks a central leader.

I'm pretty sure it's a grafted Juniperus chinensis - you can clearly see both the juvenile, needle-like tips and the longer, almost pine needled adult foliage in the second photo close up. Growth habit would support this conclusion also.

also .. since you want to learn ... its grafted on a standard ... thats the thick trunk.. that brings it off the ground ...

it also appears to be a weeper.. or a ground cover plant ... and by raising it off the ground.. it weeps back down ...

with some annual removing of a few branches.. you can maintain the look ...

ken

Thanks everyone, now I can do a bit of research and learn how to take care of it properly. I removed a few braches last year because they were basically lying on the ground. Hopefully I can get it looking good without killing it. I will have to get pictures of a few more plants on here sometime soon! Thanks again