Learn bones then muscles then blood supply/nerves. Your professor and lab TA should go in that order anyway.
For me, visualization was one of the keys to memorization. I used Visible Body's Human Anatomy app on my laptop, but you can also use
http://zygotebody.com/ which is free. The reason I didn't like Zygote Body is because I found it harder to use. There was also this Real Anatomy thing my lab professor recommended but I tried it and thought it was useless. The other thing I did was to visualize where on the body things were with my eyes closed (I'm not a visual person) and that helped me. Also, I'm definitely not an artist but I would the structures from memory (even if they were rough approximations of what things looked like) just to make sure I got things down.
So there are a lot of memory things you can do such as writing down names like
@techyguy suggests or using flash cards to memorize origin, insertion, innervation of muscles, but I think that it's really useful to think of why something is named the way it is because IMO that helps stick it in your head better. Also, functions of muscles usually just make sense if you think about the origin moving toward the insertion and how the rest of the body behaves in relation to that.
For the lab are you using models? Models are really easy to identify stuff on IMO and you can look up similar labeled models online to help you at home. I've heard some anatomy labs use other animals such as cats, and that seems not very useful to me but I guess it's an experience. For my lab we had the privilege of using human cadavers, so that made the whole thing more challenging but also more useful overall. If you're in the same boat, my best advice is to use any and all time that you're able to to be in the lab and figuring stuff out on your own--go through feeling things and figuring out what goes where until you can visualize it on your own. I found this to be the most useful time for learning. Most of my study time was spent that way, and I had less things to learn or cold memorize at home because of it.
I loved anatomy and did really well in the class. I know I spent a lot less time studying than my classmates, but I think that's because I figured out early on what worked for me and just stuck to it. Oh, the other thing I wanted to say is to take advantage of all the resources you have available (TAs, tutors, professors, etc). There's no shame in needing help to get a concept down.