Here - (sentence)

People often say "here" before offering to help or take responsibility for something. A few more examples:

Here - let me do that

Here - I'll hold this while you tie it up.

Of course, you can also use "Here" in lots of other situations, like when you give something to a person:

Here, I brought you something from Singapore.

take a look

The word "look" is very general. It can mean to look for a long time, a short time, carefully, absent-mindedly, or in many other ways. "Take a look" is more specific. It means to look at something for a short period, usually for a specific purpose.

You can ask someone to take a look at something that needs to be fixed, or for something that's important for them to see. Here's another example from a science classroom. The teacher tells the class to look at something in the textbook:

Everybody take a look at the picture on page 46. This is a model of what a strand of DNA looks like.

Let me (do something)

When you're offering to do something to help someone, you say "Let me ___". For example, when your friend arrives at an airport and is carrying heavy bags, you can offer to help carry them by saying:

Let me help you with those.

When you use the phrase "Let me ___", it's common to end the sentence with "for you":

Let me look that up for you.