The difference between the two phrases is that both can be used in the literal sense (to look in the specified direction), "look to" and "look up to" also have a figurative meaning.
The literal meaning:
Look at that, Henry's taking his first steps!
Look to your left and your right before crossing the street!
Look up at the sky, it's Superman!
Look up to your right, there's a green bird at the very top of that tree!
In all of these sentences, "look [x]" is being used to mean "look in the direction specified." This is the literal meaning of the phrases.
However "look to" and "look up to" also have figurative meanings. You can say you "look to" someone to find answers or advice, for example:
In her first few weeks on the job, Monica often looked to her boss for guidance.
This doesn't mean that she literally looked at him, but that she went to him for advice when necessary.
"Look up to" also has a figurative meaning. To look up to someone is to see them as a role model, or to view their behavior as a higher standard which you would like to achieve.
Tommy had always looked up to his baseball coach. He was tough but fair, and taught the team a lot. Tommy had wanted to be just like his coach when he was a kid.
"To look at [some thing]" means to specifically pay attention to that thing.
"To look to [some thing]" has various meanings, but in this context it means to look in the direction of that thing.
So if I say I'm looking at the parking lot, I mean that the parking lot itself is my focus. However if I just look to the parking lot, I'm just looking over toward that area with no special focus.
Similarly:
She's looking at the sky (There's something in the sky that has attracted her interest)
She's looking to the sky (She's looking generally upwards with no particular focus)
As a side note, to look to a person has a different meaning, "to hope or expect to get help, advice, etc. from someone":
I look to you to take care of the kids while I'm away.
Mary looks to Tom to cook their meals since she's been sick.
Edit: In a recent comment I wrote:
".. traders who deal in Netflix stock primarily look to subscriber statistics to determine whether they will buy or sell."
I used to rather than at, partly because I was still thinking about this question, but also to imply that the statistics aren't the only thing the traders look at -- they look at the statistics and other related data.
Best Answer
He examined her from head to toe. He could be attracted to her beauty, or looking for an injury after she fell off her bike, or he could be looking for ticks after a walk in the woods.
He looked over her head at something else in the distance.
He could be looking her in the eye, or looking on as she does something, or looking as she does nothing but stand or sit. He turned his gaze towards her.