First off, not sure if this thread should be here or in the DIY. If it should be DIY please feel free to move it.
DW and I purchased our house and it has an unfinished basement I'd like to finish someday. Where do I even start? A simple internet search returns a vast majority of ways to go about it but was hoping some of the smart folks here have done it before and have recommendations.
First, understand what you want. What is finished? Drywall, carpet, drop ceiling or drywall? Add a bath? Are you making rooms or just putting drywall around the perimeter? Are you limited by anything hanging down from the ceiling? Need to move furnace/water heater/etc or just enclose? Are you going to DIY or hire it out?
Make a plan and sketch it sorta to scale on graph paper and figure out what you want to do.
Second, need to mitigate any issues; do you get water down there? Better fix that first. Are you enclosing things that need to remain open (ceiling electrical boxes, ductwork valves, etc)? Do you have windows and if so, how do they affect your intended floorplan (i.e., need 2 points of egress for a bedroom, if you're adding a bedroom you need to make sure a window is in it.)
From there, I suggest mapping out your layout to scale on your floor with masking tape. Where are your walls going? Do you have clearance for things like doors and such? Note that a wall with two finished sides is 4.5" wide before baseboards (3.5" for a 2x4 + 2x 1/2" drywall). How are you accessing electrical panel and HVAC and other appliances down there (i.e., laundry?) If your water heater or furnace shits itself, did you put it in a place where you can move it in and out of the house or do you now need to take down a wall? Are you leaving yourself enough storage space (finished or unfinished?)
Then you need to consider finding a contractor if not DIYing it, and if you are DIYing most of it, consider where you might want a contractor (electrical? plumbing? drywall?) And consider what permits are required, or if you are going to wing it with no permits and what that means for risks and such. You'll still want to build to code even if you aren't permitting, to avoid headaches of all types later.
This is the stuff that will get you started. But there are a lot of big questions in there (DIY or not? Scope of job? Plumbing or HVAC or other significant changes?) that will direct everything else.
Edit fixed width of 2x4 typo