make an effort to (do something)

This means to "try" to do something:

I've made an effort to watch what I eat a little more carefully in the past few weeks.

You usually use it when you haven't been successful doing something, or you don't think you're going to be successful. In the example above, the speaker say that he's going to "make an effort" to spend more time with his family. That might mean that he's not really sure whether he'll be able to do that.

spend quality time with (someone)

"Quality time" is time that you spend with your family members, someone you're in a relationship with, or really close friends. It's time that you spend doing things together, like talking, playing sports together, or going out somewhere together. If you're talking to a family member and watching TV or doing work at the same time, that's not "quality time". You have to be able to concentrate on the other person.

In American culture, family members are expected to "spend quality time" with each other. If parents don't spend quality time with their children, the children may feel like the parents don't love them. Husbands and wives, as well as serious boyfriends and girlfriends, are also supposed to spend quality time with each other.

It's a common New Year's resolution to say that you want to spend more time with your friends and family.

(someone) is going to (do something)

You use "going to ___" to talk about what will happen in the future. "Going to ___" is more natural than "will" for most situations where you're expressing someone's plans to do something:

They're going to meet us at the airport.

I'm just going to stay home and relax this weekend.

English learners often over-use "will" when "going to" would be more appropriate. In general, when you want to talk about something that you've already decided to do, use "going to":

Next up is Steve. He's going to walk us through the new home page redesign.

Starbucks announced that they're going to offer free Internet access at all their locations.

We're going to keep it to just close friends and family.

If you've just decided something and want to announce your decision, use "will":

Fine! I'll take it back! 

I guess I'll thaw this out.