Activating new iphone

I disagree.

Go to An Apple store, if you don't feel comfortable doing it yourself. The Carrier should be the last option and only if the cell service is not working correctly after setup has been completed. Your carrier has nothing to do with activating the iPhone itself, only the actual service if something is wrong.

If you want to do it yourself, just follow the onscreen prompts during set up and see here for more details: Set up your iPhone, iPad, or iPod touch - Apple Support

If the OP is seeking help setting up the phone, I agree, Personal Setup at the Apple Store is a better choice. But I read the question as activating the phone in the sense of getting service on it. In that case there's nothing the store could do that the carrier couldn't do directly, and going to the carrier cuts out the middle man.

True. I just assumed they meant setting up the phone, not specifically activating cell service, which is part of setup process anyway, and can be as simple as swapping the sim card from a previous phone.

You should go through the carrier. Apple may be able to do it as well, depending on the carrier. Apple Stores support the major four carriers in the U.S. (AT&T, Verizon, Sprint, T-Mobile).