You can look and not see, but you can't see without looking :-)

I can only do it by example -  your friend can point in a direction and say "Do you see that person, that place, that thing?" .  You can look in the direction and still not see what they are referring to.

Look is an attempt, to see is to actually perceive.

Diana,

Sometimes you just have to memorize what the most common usage is by context. Here is a short list of what we usually write/say in American English.

For example:

I saw Putin's speech on TV last night.

I went to the supermarket and looked for a card for my mother's birthday!

I looked at my watch and realized I was late to my English class.

I was taking a walk and saw a man with green hair.

I can see that many people on italki are looking for English teachers.

I see my friend Masha everyday.

I watched the NBA finals.

I watch the news every night.

Did you see the Timati concert in Moscow last week?

Others:

I always like to see what's going on around me.

I always look at the nutrition information before buying snacks for my family.

 What is different between "смотреть" and "видеть?"

You forgot to ask about the verb "to watch" too.

The best way I can explain is that to look is voluntary and to see is less voluntary.

So if you say "I see a dog" you would be saying that it happened by chance. "I look at a dog" that would mean that you are doing it on purpose. 

Does that make sense?

Diana,

There's a lot more more to it. It isn't easy at all. Some of these rules are really suggestions at best.

You can look at pictures of your family for hours. You can also look at a painting in the museum for hours. The answer here is not as simple it is seems. The answer is a bit complex.

Typically, when English learners are using "see" and "look" -- they are referring to the physical act of seeing or looking with their eyes. That's not always the case though.

You can see guests to the door. This means you can accompany your guests to the door, but in this sense it means you are guiding the guest.  A blind woman can see you to the door of her home as you are leaving her party. (All without being able to see).

See can also be used in poker and other card games. See in this context means that you are deciding to match a bet initiated by another player.

See, in another sense, can also be used to describe the act of "making sure that" or making sure of something.

Ex: The nanny must see that the children are happy and well-fed.

Look after can be used as another way to say "take care of" or deal with needs of.

Ex: The oldest sibling should always look after his or her younger sibling(s).

To "look over" something means to review it. "Look over" can also mean to actually physically look over something.

In another sense, "look" can also mean to face an obstacle/problem or to try to wrap your mind around a situation.

Ex: John was forced to take a look at his own mortality after he was diagnosed with brain cancer.

You can look for something you lost, but not see it if you don't end up finding it. You will see a lot of other things in the process though!