Sometimes benjamins are better than plastic.
Cash registrations often cause delays and other problems with the logistics of setting up a race, and it's not uncommon for promoters to stop accepting cash registrations. Still, however, Promoters using RaceReady may choose to accept cash entries, depending on their policies.
You'll need to check directly with your race promoter to find out if they accept cash.
If (and only if) your promoter says it's ok to pay cash, then typically they will instruct you to show up to the registration booth and work with someone on site so they can enter you into the system on their computer. But if they want you do do something different than this, you'll want to follow their instructions rather than these:).
If you don't get into the system, you won't be scored. So you either need to use a credit card and register online, or work directly with the promoter to have them enter you into the event and pay them directly (if they accept it).