Find places online, then call to reserve. Just last week I called a place I found on Booking and found they had a room at half the price shown online. This is in France though where there seem to be rules about how rates are advertised.
Booking.com have a price guarantee, and a good one, so you will rarely get a better price from the hotel _unless you’re a member of their loyalty programme_ … so for the big hotel chains, sign up to those and book via their apps
I remember walking into a hotel at around 10 PM (I was road-tripping around Iceland and could've slept in the car too) and asking if they'd give me a discount (1 room more to sell), and the front desk person clicked around on a lot on his computer and when a colleague asked him, he said "I'll just give him the agency rate.".
The most likely reason you might get a better rate from a third-party booking site than from the hotel direct is if the hotel allows the site to do variable pricing to try to capture more willingness-to-pay; sometimes that variable pricing will work out in your favour.
They have a few mechanisms to try and drive up commission from the usual 12%, though. They have a preferred program which boosts search results but costs 3%> They would have loved to drop it to better tune search, but they were addicted to the incremental revenue.
At various times there were also dynamic ranking boost efforts, where a hotel could increase boost their ranking (with a preview) by increasing the commission percentage. IIRC that went as high as 18%.
Both of those applied to the default search results order ONLY. If you clicked "order by price" or similar then you simply got that.
(Worked for booking until end of 2017.)