I ran a small "service" business for 20 years.
I sort of fell into it naturally - started as a hobby / interest. Then friends & family started approaching me and offering to pay me to do bits for them.
From there, it was mostly word of mouth - they put their friends & family in touch with me, etc. etc.
I also put a business card or flyer in places like local shops, takeaways, pubs, etc. (a lot of them have a wall or noticeboard for local traders to stick an advert to. Some are free, some ask for £1 for the charity box).
Also the village magazine, the primary school Fete "Fundraising Programme leaflet", etc.
And keep advertising in them regularly - A common mistake is to advertise once, then dismiss it as a waste of money as you didn't get anything from it. - Then people assume you've gone bust already!
Do you have any big "shift work" type businesses near you - Would they take a flyer for the staff room?
For me - Word of mouth was my biggest "growth method"...
While the adverts did bring in a few new clients, the biggest benefit I got from those was by building up my profile and reminding people about me. Virtually everyone knew who I was, what I did and which local establishments to pop into if they needed my number!
"I saw Dave in the pub last night - he said I'd find your number in the chip shop, so I stopped there on the way home!"
Does your product or service complement another company in the same space? - Could you approach them and build a rapport and recommend each other - The local pet food supplier, for example.
Whatever you do - It won't happen overnight!
See if you can generate a bit of pocket money alongside your day job (or whatever).
If it works - Great. From that, hopefully word of mouth + continuing to advertise locally will grow it to a point you can achieve whatever level of income you hope for.
I was doing that for about 2-3 years alongside my day job before I eventually reached the stage where I could make the leap, both in terms of wages and how much of my time it was taking up.
Another advantage to this approach - doing it alongside your existing life - If you are successful and manage to get the business off the ground - it's only a matter of time before any local competition will hear about you and might try to compete with you on it. Hopefully you'll "win", but at least you've still got your old job/life to fall back on in case they win.
Going back to your original question - Research...
If you mean Market research - to see if anyone interested is in what you have to offer...
Personally, I'm not a fan standing in the street and asking people if they're likely to buy your product or service.
People without a dog will answer honestly: "No 'cos I haven't got a dog"
If you happen to catch a few shift workers - some might say "Yes, what a great idea".
Everyone else will smile sweetly and also say "Yes, what a great idea" - either because they don't want to hurt your feelings. Or because they can't be bothered to get drawn into a debate with some random about why they think your offerings aren't up to snuff!
So if I were you - I'd just roll my sleeves up and crack on - Get 1 customer.... Then another...
If you mean researching your local competition...
Trawl the local village magazines & Social Media pages from all the villages within, say, a 15 mile radius - See who your competition is.
Check out their websites to see what they're offering and if that encroaches on what you're doing...
Think about how easy it would be for them to copy your idea.
For example, if your idea is "Overnight pet sitting" - Be careful 'cos an existing "Day sitting" company could easily employ someone and offer the same thing... with the advantage that they are already an established name locally,
Depending on what you want to research - do some "Mystery Shopper" enquiries - Phone your potential rivals and enquire if they offer <your product or service>.
And don't forget to take out Business insurance.
Good luck!