I am a very new dancer. I've always wanted to take dance lessons and have had a natural talent for dance (improv dance at parties and such) but have never taken an actual class until this past month. I will say it is extremely fun and also very challenging because I'm not used to thinking about how to dance, how to move, I've always just done it. So breaking it down step by step has been a challenge, but I'm progressing.
I'm sixteen and feel very old to just start dance but I truly love it and am so glad I'm finally pursuing this dream. I know nothing about dance.
Do any of you have any advice for me? Any obvious things that I need to know about that I wouldn't know about otherwise?
Right now I'm taking a Latin and ballroom class and love it. I'm working on rumba, swing, cha cha cha, waltz, and foxtrot. Cha cha cha is my favorite so far. Thanks to everyone.

I dont know if you are boy/girl, ( partners are more available if you are a boy ) either way,one of the most important things to remember , get in as much practice time as you can, and dont restrict yourself to just your favorite dances .
Also, try as many different partners as is poss. it will develop your lead/ follow skills .

Most important.. write things down, take notes , they are good for reference .I see you are doing Amer.style (?) you may want to explore the possibility of the Intern.style as time goes on .
Very important.. make sure your teachers have a good prof.dance background and check other sources locally .

You are NOT too old! I wish someone had told me this when I was 16 and thinking all was lost! (I kick myself everytime I think I what I could have accomplished and learned by now!) If you truly love it, you'll have no problem putting in the time to practice! :)

Some of us started younger than 16, others started at middle age, or even during golden years. Starting time/age doesn't matter. If you love doing it, you'll stick with it and get as much as you want out of it. From personal experience, I also would highly recommend that you get in the habit of taking notes and writing down everything you learn. It makes practicing easier, and is great for future reference. If you stick with this, you may find yourself learning 100 or more steps for each dance you have learned. At some point, the notes come in handy to help refresh a step sequence or variation. Just writing down the name of a step doesn't always stick. I found some of my old notes from the disco era of late 1970s, and I had the names of certain moves written down, but no explanation of what the steps were! Unfortunately, I would have no idea now what steps went with those names. It's nice to kid with someone younger and say, "I've forgotten more than you'll ever know," but when that's the truth, you kind of wish you took better notes.

Sorry, I did not specify. I am a girl. And it is very good to know that its not extremely too late for me to be beginning.
I am taking both notes and videos of my classes so its easy to refer to them.
And suggestions for movements in general? Especially with the arms, I'm having trouble with those movements.

Arms take a long time to develop. The pros can work for years on one little thing until it looks just right.

Most ballroom studios offer an arm styling class once or twice a month. Take those and have someone finesse them with you. Watch tapes of other dancers, see who you like and try and work toward incorporating their styling into your own style.

Stand in the mirror and practice. Its also not just the arms but the way you move your body so your arms become extensions of your steps, the body creating picture lines, the hands in tandem with the movement of your feet. Your arms won't look good if your frame isn't good so work on that, and learn to maintain tension in the muscles. Every movement must be controlled...you can't just easily throw your arms around....it looks sloppy.

It just takes time. Be patient and know for awhile everyone looks a little bit awkward, you'll get it.