This link from Texas A&M University should be helpful. On the bottom of the page there is a section on control, both biological and chemical.

http://vegipm.tamu.edu/imageindex.html

I'm curious. Can you explain what you mean by boards that serve as traps?

I had hoped not to have to, but I did have to resort to chemicals after my 5 day vacation because the squash bugs had taken over and almost destroyed my squash, however, I only had to spray once. After that, there weren't nearly as many to deal with, so I have been able to manage the #s by hand and kill the adults, nymphs, and dispose of the eggs without spraying.
We just tried the Ivory soap thing on our tomato plants last night b/c the aphids were getting out of control. I've yet to go out this morning to check on them, so I'll let you know if it seemed to work. Ally

aulanin, the idea of putting down boards is that squash bugs congregate under them overnight as a safe place to rest. The boards need to be raised off the ground a bit. Maureen

Due to lack of boards My squash bugs congregate under the lowest old leaves which rest upon the soil. Next time you're picking squash lift up a few of the old leaves and take a peek, young nymphs like it under there too. As for control, I let them live up to their name. But it's usually the SVBorers that kill the plants here.

Can someone tell me more about the ivory soap thing. Is it bar soap or liquid and what exactly do you do with it?

Yeah...these suckers are like SUPERbugs. This is the first time I've tried to grow vegetables and I noticed them on my squash plants about a week ago and not knowing they were harmful just didn't really pay much attention until I saw groups of hard eggs on the tops of the leaves. (they lay them on the tops of the leaves and underneath near the base of the leaf) I read about them all day yesterday online and I bought some insecticidal soap from Home Depot (safe for vegetables and organic gardens) and sprayed the bugs and the plants and pretty much killed all of them. I went back and checked later last night and no more had came back so it seems to be very effective. The key is to control the adults before they lay eggs, and if you see the eggs, crush them before they hatch.

I agree with lexie, the key is squashing the eggs. I didn't know what to do last year, but this year I noticed the eggs. Squash bugs and cucumbers beetles lay clusters of brown or lighter brown egg eggs laid on the undersides of the leaves and the stalks as well. I've noticed they lay the eggs the "armpits" between the leaf and stalk, so they hard to get out. Tenacious buggers! Good luck. Now is a good time to start scouting, as many things hatch near the beginning of July.

Neem works if you get a direct hit, but once it dries it doesn't help. Any recommended chemicals that don't need to contact to kill? I have board traps (few caught), marigolds (caught them screwing on the flowers), and just spent an hour crushing eggs and smashing adults. Guarantee that I can go out right now and find a half dozen nests and a few adults.

Squash bugs like to hide in mulch during the heat of the day. Remove all mulch near the plants. Maureen

Maureen, thanks for telling me what board traps are. I'll have to remember that.

I read on another thread that a good way to get the eggs is with masking tape. Makes sense. So far so good for me on squash bugs. I had used a prophylactic dose of sevin on the stems and nearby soil early on and they seem to be staying away. I'd better knock on wood. But I do check every day.

Another GW poster & I had discussed home-made sprays to kill soft-bodied insects. The post has apparently passed into the Happy Place Where Old Posts Go...which is really a shame, there were some good dos & don'ts mentioned, as well as several useful formulas. I saved one of them as a clipping, so I will re-print it here:

"It was only after reading this thread that I remembered saving a couple of recipes last year -- recipes which would have been useful this year if I had remembered sooner.

INSECTICIDE: A U.S.D.A. formula combining oil and soap is effective in killing soft-bodied insects. Mix 1 cup peanut, safflower, corn, soybean, or sunflower oil with 1 tablespoon liquid dishwashing detergent. To make the spray, use 11/2 teaspoons of the oil-detergent mixture for each cup of water.

SLUG DOUGH: According to our friends at Organic Gardening, a great bait is a home brew that can be kept in your refrigerator: 1 Tbs. Molasses, 3 Tbs. Cornmeal, 1â2 c. flour, 1â2 c. water, and 1â2 Tbs. Yeast." (Jimster)

(The slug dough may not pertain to the OP, but since it is useful & part of Jimster's post, I've included it also).

I have used a similar spray to control squash bugs, with 1 tsp. of sugar added per quart of solution. The sugar blocks their spiracles (the holes they breathe through) even after the soap solution has dried. Provided that the bugs are soaked completely, they die very rapidly. This works on both adults and nymphs... I believe it kills the eggs too, but I can' be certain.

This spray is for spot applications only, not for broad coverage. It can cause some leaf burn. If applied widely, it should be washed off once the bugs have died, about 30 minutes later. Avoid using it on sunny days, which can accelerate the leaf burn.

By the way, with the addition of more sugar (1 tbsp. vice 1 tsp.), this solution will also kill cucumber beetles, as long as they are covered completely. To avoid damage to foliage, knock the beetles to the ground with a slap to the infected area, and spray them there. Do so quickly, before they have time to fly.