I don't really have to means to test or engineer the product. I am wondering if it is possible to hire someone who can just help me articulate the idea and register it as a patent.
Yes, it's possible. All that is needed is that the application describe your invention in enough detail that it would enable someone of ordinary skill in the relevant technology/ies to make and use your invention.
How much might this cost (getting a patent attorney or such)?
There are primarily two phases.
The first is preparing and filing the application. That cost depends entirely on the complexity of the invention and starts at around $3k for very simple inventions and up to $20k or more for particularly complex inventions. I think it's useful to consider complexity in terms of the number of parts that require description and a multiplier for degree of difficulty for technologies that require careful navigation of the law. For example, I recently had to deal with the definition of "the application layer" in the OSI model for computer communications. It was very tricky to work that definition given that many will try to read "application layer" as any layer at which applications are present.
The second is prosecution of the application -- arguing with the Patent Office over whether your application should be granted and a patent issued. That depends entirely on actions by the Patent Office and can cost anywhere from a few hundred to several thousand depending on the nature of the action. Those actions typically won't start happening for 2-3 years after filing, but they do happen and the Office will really put your through your paces in showing that your application should be granted. The good news is that the costs are deferred for a few years and those years should tell you something about the value of your innovation.
Is it safe to just give an idea to a patent attorney and let them research it and put in a patent application?
Yes and no. You'll have to read the application and sign some papers about it. And, the attorney won't be as familiar with the relevant technology as you are, so you'll have to make sure they get the description of your technology right. The attorney should give you some guidance through the process.
Can someone give the names of a few trusted agencies I could go to?
Many of the posters here provide precisely the service you're looking for, so I wouldn't expect them to recommend others nor to recommend themselves (to avoid appearing too self-serving).
Even if the agency is trusted, should I still have them sign some kind of confidentiality agreement before presenting the idea to them?
For an attorney, the obligation to keep your invention secret is more binding and persuasive than any NDA you would have them sign. So, such an agreement would be superfluous, but wouldn't hurt.
The price of the patent process is what I most would like to know, so that I can know how much I need to be prepared to spend.