When it comes to talking about plans and things we want to do (intentions) we usually use "be + going to + verb". When speaking quickly, "going to" sounds like "gonna"*. 

Usually these things will happen near the time of the conversation. This includes plans which are or aren't yet confirmed:

I think I'm going to give Tom a call tonight. 

They're going to take a vacation later this year.

I’m going to eat pasta later tonight, so let's get sushi for lunch instead.

*It is inappropriate to write "gonna" on any exam writing task. Also, in real-world situations, writing "gonna" can make you appear lazy or uneducated to native English speakers, so use it wisely.

We also use "be + going to + verb" when making predictions based on current evidence:

There's a lot of dark clouds in the sky and the wind is picking up. I think it's going to storm.

Judging by the photo, it looks like they're going to have a party. 

It looks like he's going to go on a trip.

It's more common to use will when talking about predictions, especially those in the distant future. We also often use words like "I think" "I believe" "probably" "maybe" and "possibly" with these phrases:

In 50 years, we will probably live in man-made cities that float in the middle of the sea.

I'm pretty sure that my party will win the upcoming election.

Maybe someday I will live and work in an English-speaking country.

Here, we can also use be + going to + verb:

I think my team will win the game.
I think my team is going to win the game.

Someday I will buy a nice, big house.
Someday, I am going to buy a nice, big house.

We also use "will" to express a willingness to do something:

If you want, I'll go first during the speaking task.

I know you spent a lot of time cooking so I’ll do the washing-up.

That bag looks heavy. Don't worry, John will carry it for you.

We use Present Continuous to talk about arrangements. These are often arrangements made with other people, such as appointments, meetings, and events. They are confirmed and should happen:

This weekend I'm having dinner at my parents' house. 

They're getting married next month. 

Next month, I'm going on a business trip.