Here are three ways...
1. Start with what you know.
That is, what are your hobbies and interests? You won't necessarily pick one of these niches (you need to check if they're profitable and viable first), but add 'em to your "possible markets" list.
Example: I go on CraigsList and look at these old Corvettes and wonder if I could restore them. Corvette DIY restoration -- that's a market.
2. Use a keyword tool.
Plug in extremely vague searches like this:
get rid of
You'll come up with hundreds if not thousands of ideas. Add 'em to your "possibles" list (later on you'll have to research 'em).
Real examples that may give you ideas:
How to attract an Aries man
How to make a crossbow
How to write a resume
How to get rid of ants
How to get rid of an ear ache
How to get rid of THC in the body
How to get rid of bed bugs
3. Listen. Observe. Brainstorm.
My sister just got a goby fish -- my first thought was, "that's a market." She also went to the casino last weekend -- more possibilities there.
I have friends planning summer vacations -- just like thousands of others are doing right at this moment. Lots and lots of niche market possibilities there.
I know someone who has early alzheimers, and her daughter is struggling to come to grips with it. She's been doing a lot of research about how caretakers can cope. That's another niche market possibility.
Think about the changing seasons and you'll find plenty of ideas -- yard care, gardening, pest control, getting a "bikini body," grilling tips and recipes, etc.
And so on. Really, there are big markets and corresponding smaller niches EVERYWHERE, if you just open your eyes and ears.
I keep a notebook and write 'em down when I first hear about them. Then later I do the required research to see if they're worth pursuing.
Those are just a ways to come up with ideas for possible niches. Please do add your favorite methods to the list.