You need to send it away for testing - it would be impractical to home test for all of the things you'd want to test for.
It's likely that your local municipality has a testing service that you can send water into for $50 or $100 and have rough testing done for lead and e-coli and crypto and so on.
A more extensive (and expensive) test will test for essentially everything, including VOCs and chemicals and all manner of manufacturing byproducts, plastics, phthalates, etc.
That would cost you $600 or $800 ...
I do have 65 ppt of PFAS in my well water (one of the gray dots in West Michigan, where Wolverine operated a tannery that dumped Scotchguard-treated leather scrap in local swamps). The test for that (and various other contaminants) ran $650. Yeah, Wolverine is paying for that and the carbon filters in my basement, but it kinda sucks to have been drinking it for 30 years. At least they caught it when my kid was onky exposed in the womb and his formula until he was 1...
A few hundred dollars will get you a lab test for common contaminants, but the cost rises exponentially for anything beyond that.
Just curious.