I'm brand new to yoga.

[Bealofull]

Which video's on youtube are you watching?
I personally can recommend Yoga with Adrienne. I believe she is quite good with giving pointers to check your alignment, making sure you stay physically safe.

There are a few things that you need to pay attention to, as there are a few fragile points in the body (neck, back, knees). So for example, in the Sun Salutation above (thanks The Necromancer, that is a really clear picture!), in hand to foot pose, make sure you bend from the hip, not the back. Don't force yourself further down then where you can go, if you can't reach your feet yet, you simply can't right now. In pose 4 and 9, keep your knee above your ankle, don't go too far forward or sideways. In pose 5 and 8, keep the fleshy bit between your thumb and pointy finger on the mat, don't let it lift and collapse your weight in your wrist. In Cobra, don't lift your shoulder to your ears, keep them down.
They might seem like small subtle things, but it really will help avoid pains and aches!

It would be great if you could get to a teacher you could adjust your poses, but if you can't, make sure you read up a bit, but most importantly, listen to your body! Try out different subtle small muscle movements, see what feels best.