Carp fishing isn't terribly difficult, nor does it entail expensive or complex gear. Lots of different rigs you can use. I personally light light setups for carp.
For me it's hard to beat a simple hook & indicator setup - I use a short shanked hook like an octopus, or straight eye saltwater type bait hook. I avoid long shanked hooks, especially for carp. My indicators are large corkies - you could use the small thill sliding floats meant for panfish or fly fishing strike indicators, but corkies are cheap and they work great. I use the large sizes. Peg the corkie onto your line using a section of tooth pick. Peg the corkie with the tooth pick pointing toward your hook to help avoid tangles when casting.
Bait, for me, is bread. Whole grain, multi grain, wheat - I buy what is on sale. One loaf is way more than typically needed even for a full day of action packed carping. Tear a square off the slice and press it firmly around the hook - you're burying the hook into the bread. Dried, stale bread sucks for this, and should be avoided. Keep your bread bag closed during fishing so the bait doesn't dry out.
I like using long, limber rods for this, as casting is typically a lob cast. I will use a fly rod for this, and a spinning reel, or you could even use a fly reel for more sporting battle. I have done so - and a carp will take you into the backing in a heartbeat!
Set the indicator at the water depth or just a bit deeper. You do NOT want to try suspending the bait under the float. The bait should be on the bottom with just a bit of slack between the indicator and the bait. This allows the fish to mouth the bait and begin swimming off before the corkie bobbles. Don't expect the corkie to just pop under water like you would for trout or panfish - usually when a carp takes the corkie will start swimming off. Give the fish a second to swim then hammer him and hold on. Make sure the drag isn't set so heavy as to break the line, as the fish will RUN when hooked.
The biggest obstacle to this method - you want to find actively feeding fish. This is NOT a blind fishing technique, I don't simply lob a bait out and hope something swims by. I look for signs of fish feeding - tell tale bubble trails, clouds of silt, or even look for cruising fish in water clear enough. Cast near to, but not directly onto, feeding fish. Cast ahead of a feeding fish - anticipate their direction of travel. If there's a pack of fish working so much the better - cast close. The fish will find the bait easy enough. I typically fish shallow water, close to shore. Carp can be found in very shallow water, I've spooked them sitting up against the bank before.
The other methods - hair rigs, carolina rigs, drop shot rigs - they will all work. Hair rigs are interesting because the fish tend to hook themselves, but this means you're using a good amount of lead, and frankly I hate lobbing heavy lead. I like keeping junk off my line whenever possible and maximizing sensitivity and feeling when fighting the fish.
You can get creative and make your own boilies, you can buy pre made stuff at some tackle shops, or you can use bread. I haven't found corn to be a great carp bait - but pikeminnow love the stuff. You can use carp specific tackle, baitrunner type reels, ultra long rods with limber tips, or you can use whatever you have. If I'm out for real fun, I use ultralight spinning tackle and 4lb test line. Biggest carp landed on such was about 20lbs. Normally though I like 10lb mono and a limber fly rod or spinning rod of 8-10 feet. Steelhead float fishing rods work great for the hook/indicator method. For lead slinging - a steelhead drift rod say your typical 8'6" to 9' bait caster works well.
Use what you got though - don't feel you need to buy a special carping' rod, unless you want to.
FYI - carp fishing at Bethany pond has gone downhill in recent years. Not sure if it's something that THPRD has actively pursued, or if it's natural population fluctuations, or what the deal is. Fishing on the Tualatin River at Cook Park is good though - and the regs have changed this year and now the river is open year round to angling. There are some tall pylons set into the riverbed just downstream of the boat dock - I fish right by those as there are almost always carp milling about in that area - usually no more than 20 feet or so off the bank. That is the very place I was taught to carp fish by an old European immigrant who was fishing for food. When I met him, he had a big wire basket full of fish, and some fish were far too big to fit in the basket, and there were a number of them laying on the ground next to his basket of fish - he was very good. The setup he used was a fly rod, spinning reel, and no weight. He didn't even use an indicator - he watched the line. When it twitched or began to come tight, he set the hook. I have done this and done well, but the indicator is easier for the lazy man.
