It's hard to say. Generally, take denotes an active action, like "I took his cheese," while get denotes a passive one, like "I got my paycheck today." Besides that, you just have to memorize which one to use where.
Examples of take:
- I take a shower.
- I take it that you're going. (Meaning: From what I can tell, you are going.)
- I take my pills daily. (Action of consuming.)
- I took your cheese. (Physical removal of an object.)
- The main point I took away from that was... (understanding a concept)
- I took her to the opera. (Conducting someone.)
- I took up doing cocaine. (to start a habit)
Examples of get:
- I got my paycheck. (Received from someone else giving it to you.)
- I get you. (As in, I understand you).
- I didn't get that, please repeat it. (As in, I didn't hear).
- Get out of here.
- Get dressed. Take your time. (From PyroTiger).
- Get up!
- Get a life.
I could go on. You can check dictionary.com's entries on take and get for more.
If someone says "I have a book of photographs by Diane Arbus", and you respond with "Can I see it?" or "Can I look at it?", there is no difference in meaning. "Look at" and "see" in this case mean the same thing: "I want to view/inspect the photographs/book."
If someone says, for example, "Did you want to speak to John? He's at Willie's Bar and Grill right now", and you say "Let's go (to) see him", it means "Let's go to Willie's Bar and Grill to visit John and talk with him", but if you say "Let's go to look at him", it means "Let's go to Willie's Bar and Grill and view/stare at/inspect John". John is being considered a person in the first sentence but an object (like a book of photographs or a statue) in the second.
In some languages, one verb is used for "look", "read", and "see" (Chinese speakers in Taiwan, for example, use the verb "kàn" (看) for all three even though there are three different verbs for those three English words. What "kàn" means in a particular sentence, though, depends on the context and what question it answers.
In English, "looking at a book", "seeing a book", and "reading a book" have three different meanings. To "look at" means to "inspect/view", to "see" means to "perceive with the eyes", and to "read" means to look at and (try to) "understand the words in the book" (the content/meaning).
Best Answer
The difference between "have a look" and "take a look" is geographical rather than semantic. The former phrase is usually used in the UK, whereas the latter is usually used in the USA. (I am an American who has lived in the UK for 24 years.)