Which section is the crossword puzzle in? Do you want to run the ad local only? I'm betting all you need is one column, and say maybe five lines for your cryptic text and another 5-8 for that cat image. Does the rate calculator help you now?

Former newspaper advertising goddess here, although not for that paper.

The crossword puzzle is in the Living section, which would fall under ROP rates. (ROP = Run Of Press/Run of Paper. This covers all advertisements that run in the regular paper, not in the classified section or inserts.) When I looked at the ROP rate card, it looked like the rates online were contract rates - you don't want that for a one-time ad. I can also tell you there can be almost as many pricing possibilities as there are ads in the paper! Rates can vary for the amount of days you run, whether or not your ad is camera-ready, etc. etc. Your best bet is probably to contact someone in the retail advertising department (list here and let them know what you are looking to do. Don't worry if the rate card looks super-confusing. A sales rep should be able to explain to you in plain English what it all means and what the packages are. I know when I worked at the paper I made my own rate sheet explaining some of the more popular packages in a much clearer way. (A lot of the reps did that)

Former newspaper worker here too. But not for this newspaper.

You can throw out a pile of the terms -- they apply to campaigns, agency representation, contracts for repeated ad insertions, and so on. And some of them are obvious. Here's my interpretation of the remainder. (Did I mention that I don't work for the Oregonian?)

1. Pay in full in advance or they cancel the ad.
2. Your camera-ready ad has to include a border around it. (In my experience, a border of any kind, even if it's a chain of teddy bears. But you SHOULD ask.) The newspaper can insert the word 'ADVERTISEMENT' if they think it's potentially ambiguous.
3. Item I probably won't apply to you, since you're running a single insertion and you probably know how much space to take. It amounts to how the newspaper will handle your using less space than you paid for. Best to ask them directly if you have any qualms. In my days at my newspaper, if somebody paid for a 1x4 ad and gave us a 1x2 image, we knifed it up so that it fit all four inches. Yes, knife. It was a long time ago.
4. You have to place the ad on your own behalf. As opposed to, say, working as a proxy for a titty club that's been banned from the entertainment listings.
5. If the publisher screws up your ad, they're only liable for the cost of the placement. You still have to pay if your ad is run but not exactly where you requested.

In short: Buy early, pay immediately, and deliver the artwork before deadline, lest you be bumped by a filler about finding your next job through the Classifieds.

You say that you want to run a 'cryptic' ad: Make its meaning clear to the ad rep when you buy the space, or face the risk of a nervous ad manager or editor pulling the ad just before press time. These days, the primary fear is terrorism, but back then they were mostly afraid of something like a ROT13'd string of obscenities or libel.

sisterhavana's advice was good, but here's a tip from a former production worker: Make your ad exactly the size you buy for, in the proper dimensions. The newspaper should have a template sheet or file with standard sizes. Back in the day we had one regular client run new ad art every two weeks, and every fortnight it was the wrong size: If he bought a 2x5 ad, we would receive 2.5x3.25 artwork. That is, he bought a rectangle 2 columns wide (roughly 3.25 inches) and 5 inches tall, and sent us art 2.5 columns (5") wide and 3.25 inches tall. Weirdly, he never complained about his designer's nice art always ending up torn apart with meathooks, and as far as I can tell the rep never heeded our pleas to tell the client what was wrong.

OK, I'll give the ad department a call after the holiday. Thanks!

(And by "cryptic" I really just mean "not advertising anything in particular" because, well, I'm easily amused. But I'll make that really clear with the ad rep)

I hope you're willing to share the ad once it's published, cmonkey. I'm intrigued!