Aside from interviews and basic research, what is the overall process like to gather information and report the story?

The process depends very much on the story. If the story is crime-related, you interview police, bystanders, victims. You check statistics in the official records. You can do some research on the internet, but not everything online is accurate.
For sports, get to know the coaches, players and staff. If they trust you, they will give advance notice of events and keep you up to date on the situation. Also, people who trust you will feed you tips for stories and features.
Do Not violate someone's trust. If people do not trust you, they will not give you information.

The process off getting and reporting a news story involves a number of aspects, including the two you have already identified.

First, pose a question you want to answer. Then think about whether it is something your readers/viewers/listeners would also want to know about. You will often find that anything you wonder about yourself, any question you can think of about a subject, is also something that someone else is wondering about. And that's how you choose the topics of your stories - would people want to know more about this? If the answer is yes, then pursue it.

Next, consider the questions that need to be considered in relation to the story. This means sitting back and thinking about specific details and whether they are important enough to become a news story. Some will be obvious - Who won the game? How much money is in the budget? Who won the election? But then think beyond the obvious facts. How did they win the game, with a new strategy or an old one? Why is the budget bigger than last year, what is the money being spent on? Who and where did the votes come from that helped the candidate win?

Then you get to work on the aspects of the story that you have already mentioned in your question - doing basic research and asking questions of people who may have the answers. You need to get the basic facts and background on your own before asking questions of anyone. For instance, if a religious figure comes to your city for an official visit, you should take the time to look up all the basic information about that religion and that person's position before going to interview him/her. You should be prepared with specific questions and not expect someone to give you a lesson in the basics. If you are doing a story about the new city budget, your first question should not be, "How do you write a budget?"

After you have the basic research completed, you begin contacting people and asking questions - not only the obvious people, but anyone you can think of who may have some information that will be helpful. Even if you only have one question for them, the answer may lead to more questions and more information. Everyone and anyone has the potential to be a good source of information for a story.

Common sources for journalists are the people who work on a daily basis in whichever field you are covering. Get to know them, not just when a story breaks, but also on a casual basis so that you are already acquainted and you don't have to go through the time of introducing yourself if you are rushing to meet a deadline. Plus, once you get to know people then they are more likely to trust you and share information with you than if you are a stranger stepping foot in their office or workplace or home for the first time.

You should get to know the principal figures who have the most information. If you are writing political stories, you should be in regular contact with the people in office at whatever level you are covering - town council and school board members, mayor, governor, congressmen, senators, etc. If you're covering police and fire - chief, captains, lieutenants. If you cover education - university officials, school district superintendents, school principals, teachers. Stop by their office or place of work on a regular basis so they get used to seeing you. And every time you visit, ask them general questions - What's going on where you work right now? What are the current goals and projects you have? Remember to ask specific questions - if you just say, "What's happening?" then most people will saying, "Nothing much." You have to ask for the information that could lead to a story: Is there anything happening you think people should know about and needs to get some coverage in the news? Are there any new people I should meet? Are there any upcoming events? Have there been any changes recently? What are you planning to do next week or month?

Also get to know the people who work for and around the "important" people - the assistants and staff members, the secretaries, the clerks, the street cops, firemen, the people at the front desk, the person who schedules appointments, security guards, park rangers, janitors, the guy or lady who runs the coffee shop on the corner. Say hello to these people. Get to know their names. They might be in a position to help you learn something important in the future. (Plus it's just nice to get to know people around you.)

After you have talked to everyone you should or can and compiled your information, begin by writing up a list of the the most important information from top to bottom, most to least important. (This, of course, always depends on the amount of time you have before your deadline. NEVER miss your deadline.) Remember, the most recent piece of information is not necessarily the most important piece. Make sure you are clear on the most important aspect of your story before you begin writing/taping and put that at the top, or else you may end up putting something that most people consider to be valuable somewhere in the middle. This is very annoying to anyone who wants the important news quickly and doesn't necessarily have the time or desire to stick with your entire story all the way through. Putting the most important information further down is referred to by journalists as "burying the lead (lede)" and it doesn't help a story. Even if you are doing a longer piece and want to set the scene with some description or explanation, keep in mind that people will be looking/listening and wondering, "What's the news here? What's important? Why is this worth my time?" If you take too long to get to that, you will lose them and your big, important story may be ignored.

Finally, make sure you proofread/review all your facts and, if you are in print journalism, your text to make sure you haven't made any mistakes. There is no sense in doing all that work to compile a great story and then letting small or silly factual mistakes or typos get through to the final version.

After you have published/broadcast/posted your story, be ready to do a follow-up. Perhaps more than one. After people have seen your story, there may be someone who comes forward with more information, or information that corrects/changes something in your story. Remember, journalists are human. If you were not able to tell the whole story the first time around, then be willing to update it. And if you make a mistake, have the honesty and integrity to correct it. Do not try to cover up an error or change the story to make your version look true. In journalism, mistakes can be forgiven, lying cannot. And even if you are eventually forgiven for not being truthful, it will never be forgotten. To paraphrase an old saying - it takes years to build up a good reputation, and only a moment to ruin it.

Overall, be curious, be thorough and be honest. Remember, you are doing a public service by providing information to people who don't have the time or power to find it out for themselves.