Is the goal accumulating status? i.e. a mattress run? In that case - seek out locations with low nightly rates. If you're based in the US though, just get one of the Hilton credit cards that gives status.
If you are asking in general - then it's checking/booking special rates that you can qualify for: e.g. AAA/CAA rates, Corporate Rates (your own employer, a client's employer, a professional organization that you're a member of, etc). You can enter the group code/promo code/corporate account code directly into that "Special rate" box booking directly with Hilton's website or app.

There are also programs like AMEX FHR that have rates with special perks (e.g. $100 hotel credit). Or 3rd night / 4th night free, etc. But these programs are more about "better value" , not "cheapest".